BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Critical point in system of interacting bosons DTSTART;VALUE=DATE-TIME:20240924T072000Z DTEND;VALUE=DATE-TIME:20240924T080000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-308@indico.bitp.kiev.ua DESCRIPTION:Speakers: Mark Gorenstein (Bogolyubov Institute for Theoretica l Physics\, National Academy of Sciences of Ukraine)\nA system of bosons s tudied within the mean field framework has two fascinating phenomena: a li quid-gas first order phase transition and Bose-Einstein condensation. Inte rplay between these two phenomena is being investigated. Depending on the mean-field potential parameters one can observe two types of critical poin ts (CP)\, called ”Boltzmann” and ”Bose”\, that belong to different universality classes with distinct sets of critical exponents. As example s of Bose and Boltzmann CPs pion and α matter are considered\, respective ly. In general\, the phase diagram can have one of the CPs or both of them .\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/308/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/308/ END:VEVENT BEGIN:VEVENT SUMMARY:AdS/CFT correspondence and and classification of Kaluza-Klein mod es within the supergroup DTSTART;VALUE=DATE-TIME:20240924T135000Z DTEND;VALUE=DATE-TIME:20240924T135500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-346@indico.bitp.kiev.ua DESCRIPTION:Speakers: Tetiana Obikhod (Institute for Nuclear Research NAS of Ukraine)\nWithin the framework of AdS/CFT correspondence we considered large N limits of conformal field theories in d dimensions which described in terms of supergravity on the product of AdS space with a compact manif old. An important example of such correspondence is equivalence between N = 4 super Yang-Mills theory in four dimensions and Type IIB superstring th eory on $AdS_5 × S^5$ [1]. The confirmation of this correspondence comes from the fact that the Kaluza-Klein modes of type IIB supergravity on $Ad S_5 × S^5$ coincide with the chiral operators of N = 4 super Yang-Mills theory in four dimensions. Moreover\, to describe N = 4 super Yang-Mills t heory in four dimensions\, one should use low energy supergravity on $AdS_ 5$ and the infinite tower of massive Kaluza-Klein states on $AdS_5 × S^5$ [2]. The supersymmetry group of $AdS_5 × S^5$\, is known to be the same as the superconformal group in 3+1 spacetime dimensions. So\, the supersym metries of Type IIB superstring theory on $AdS_5 × S^5$ and Yang-Mills t heory in four dimensions are given by the same superconformal group SU(2\, 2|4). We presented the Kaluza-Klein masses and their multiplet classificat ion corresponding to the superconformal group representations.\n\n1. Edwar d Witten. Anti De Sitter Space And Holography. Adv.Theor.Math.Phys.2:253-2 91\,1998.\n2. Juan M. Maldacena. The Large N Limit of Superconformal Field Theories and Supergravity. Adv.Theor.Math.Phys.2:231-252\,1998\n\nhttps:/ /indico.bitp.kiev.ua/event/13/contributions/346/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/346/ END:VEVENT BEGIN:VEVENT SUMMARY:Orbital perturbation theory in Schwarzschild space-time DTSTART;VALUE=DATE-TIME:20240926T133000Z DTEND;VALUE=DATE-TIME:20240926T135000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-327@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksii Yanchyshen (Bogolyubov Institute for Theoret ical Physics)\nIn our work\, we obtain a set of Gaussian orbital perturbat ion equations in the Schwarzschild space-time in terms of Weierstrass elli ptic functions\, and solve it for several external forces in linear approx imation. We consider forces defined from: the cosmological constant in the Schwarzschild–de Sitter space-time\, various quantum gravity correction s\, angular momentum from the Kerr space-time and some others. From this w e obtain several observables\, in particular\, we consider a simple "kludg e" scheme for gravitational waveforms.\n\nhttps://indico.bitp.kiev.ua/even t/13/contributions/327/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/327/ END:VEVENT BEGIN:VEVENT SUMMARY:Milky Way globular clusters in cosmological timescale. Probability of the interaction with the Galactic center DTSTART;VALUE=DATE-TIME:20240926T131000Z DTEND;VALUE=DATE-TIME:20240926T133000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-320@indico.bitp.kiev.ua DESCRIPTION:Speakers: Marina Ishchenko (MAO NAS Ukraine\, 2 Fesenkov Astro physical Institute\, Observatory 23\, 050020 Almaty\, Kazakhstan 3 Nicolau s Copernicus Astronomical Centre Polish Academy of Sciences\, ul. Bartycka 18\, 00-716 Warsaw\, Poland)\nThe main idea of the work is to carry out t he dynamic evolution of the orbits of Globular Cluster (GC) subsystems sam ple lookback time up to 10 Gyr. This allows us to estimate the possibility of GCs interaction with the Galactic center that dynamically changed in t he past. To reproduce the structure of the Galaxy in time\, we used extern al potentials which dynamically changed in a past and now their characteri stics are similar to the physical values of the Milky Way at the present d ay (mass and size of disk and halo). External potentials were selected fro m the large-scale cosmological database IllustrisTNG-100 (TNG-TVP). In the se potentials\, we reproduced the orbits of 147 GCs from Gaia DR3 in 10 Gy r lookback time using our own high-order N-body parallel dynamic code phi- GPU code. To identify clusters that have interaction with the Galactic cen ter\, we used the criteria of relative distance: it must be less than 100 pc. Applying this simple criteria\, we obtained statistically significant rates of close passages of the GCs with the Galactic center. We identified ten GCs\, including NGC 6401\, Pal 6\, NGC 6681\, NGC 6712\, NGC 6287\, N GC 6642\, NGC 6981\, HP 1\, NGC 1904\, and NGC 362\, with a high probabili ty of close passages near the Galactic center in all four TNG-TVPs\, parti cularly the first six with a probability of around 100%.\n\nhttps://indico .bitp.kiev.ua/event/13/contributions/320/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/320/ END:VEVENT BEGIN:VEVENT SUMMARY:Initial value problem in the case of multivalued dispersion equati ons DTSTART;VALUE=DATE-TIME:20240926T125000Z DTEND;VALUE=DATE-TIME:20240926T131000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-330@indico.bitp.kiev.ua DESCRIPTION:Speakers: Serhii Kukhtaruk (V. E. Lashkaryov Institute of Semi conductor Physics NAS of Ukraine)\nDispersion equations and relations are the key subjects of linear theories involving waves and collective excitat ions. However\, in some systems\, dispersion equations contain multivalued functions and their solutions are ambiguous. To resolve such uncertainty we suggest analyzing the initial value problem that gives the unambiguous solution. \nAs an example\, we considered the excitation of the Dirac plas mons in graphene on a polar substrate and analyzed a strong coupling betwe en plasmons in graphene and surface optical phonons of the substrate. Due to square-root singularity in graphene polarizability [1]\, the dispersion equation for this system contains branch points on the plane of complex f requency\, $\\omega$. The use of the initial value problem gives a unique solution and clarifies the physical picture of coupled oscillations. Parti cularly\, we found that lower plasmon-phonon mode\, which in terms of disp ersion can have a good quality factor\, is almost absent in excitation spe ctra. The main physical reason for the mode collapse is the suppression of space-time-dependent electric fields near $\\omega=v_F k$\, where $v_F$ i s the Fermi velocity and $k$ is the plasmon wavenumber [2]. The evidence o f the collapse can be seen in the relevant experiments [3\, 4].\n\n[1] S. M. Kukhtaruk and V. A. Kochelap\, Phys. Rev. B **92**\, 041409(R) (2015).\ n[2] S. M. Kukhtaruk\, V. A. Kochelap\, V. N. Sokolov\, K. W. Kim\, Physic a E: Low-dimensional Systems and Nanostructures\, **79**\, 26\, (2016).\n[ 3] R. J. Koch\, T. Haensel\, S. I.-U. Ahmed\, Th. Seyller\, and J. A. Scha efer\, Phys. Status Solidi C **7**\, 394 (2010). \n[4] R. J. Koch\, Th. Se yller\, and J. A. Schaefer\, Phys. Rev. B **82**\, 201413(R) (2010).\n\nht tps://indico.bitp.kiev.ua/event/13/contributions/330/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/330/ END:VEVENT BEGIN:VEVENT SUMMARY:Pauli resonances in single- and many-channel systems DTSTART;VALUE=DATE-TIME:20240926T121000Z DTEND;VALUE=DATE-TIME:20240926T123000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-365@indico.bitp.kiev.ua DESCRIPTION:Speakers: Victor Vasilevsky (Bogolyubov Institute for Theoreti cal Physics)\nIn this report\, we present results of systematic investigat ions of peculiarities of redundant solutions of the resonating group metho d (RGM)\, which are known as the Pauli resonance states. Such resonance s tates appear when one tries to use more advanced (more precise) wave funct ions describing internal structure of interacting clusters. It is generall y recognized that the Pauli resonance states are spurious solutions which blur real physical quantities such as phase shifts\, cross sections. Their appearance cannot be attributed to enlarging of centrifugal and Coulomb b arriers\, they also appear in a single-channel approximation and thus the Pauli resonance cannot be considered as the Feshbach resonances.\nThe subj ect of our investigations is continuos spectrum states of light nuclei $^ {6}$Li\, $^{7}$Li\, $^{8}$Be\, $^{9}$Be and $^{10}$B\, which are consid ered as two-cluster systems. Special attention is paid to the Pauli resona nce states which appear in interaction of $^{6}$Li with neutrons\, deuter ons\, tritons and alpha particles. All investigations are carried out in a three-cluster microscopic model\, which was formulated in Ref. [1]. In th is model dominant three-cluster configuration is transformed into a set of binary channels. One of the constituents of the binary channel is conside red as a two-cluster subsystem. Spectrum of bound states and corresponding wave functions of the subsystem are obtained by solving the two-cluster S chrödinger equation. This allows us to use more adequate wave functions d escribing the internal structure of the two-cluster subsystem. This is rat her important for two-cluster subsystems with a small separation energy\, such as deuteron\, $^{6}$Li and so on. Within the model\, Gaussian functi ons are used to describe relative motion of clusters in bound states of a two-cluster subsystem and oscillator functions are utilized to expand wave function of continuous spectrum states of compound nucleus. At the first stage of our investigation\, we use single-channel approximation in order to detect and analyze the Pauli resonance states.\nIt is found that the Pa uli resonance states in selected nuclei lie in the energy range between 11 and 45 MeV\, and their widths are varied from 8 keV to 8 MeV. The most d ense area of resonance states are concentrated in the interval 16 \n\nhttp s://indico.bitp.kiev.ua/event/13/contributions/365/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/365/ END:VEVENT BEGIN:VEVENT SUMMARY:Elastic form factors of light alpha-cluster nuclei DTSTART;VALUE=DATE-TIME:20240926T115000Z DTEND;VALUE=DATE-TIME:20240926T121000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-323@indico.bitp.kiev.ua DESCRIPTION:Speakers: Borys Grinyuk (Bogolyubov Institute for Theoretical Physics)\nWithin the α-particle model\, the structure of $^{12}C$\, $^{16 }O$\, and $^{20}Ne$ nuclei is studied. With the use of the variational met hod with Gaussian basis\, the wave functions are found for three-\, four-\ , and five-particle systems consisting from α-particles. The charge densi ty distributions and elastic form factors of $^{12}C$\, $^{16}O$\, and $^{ 20}Ne$ nuclei are calculated within the Helm approximation.\n\nhttps://ind ico.bitp.kiev.ua/event/13/contributions/323/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/323/ END:VEVENT BEGIN:VEVENT SUMMARY:Towards relations between compaction and compressibility of hard s phere mixtures DTSTART;VALUE=DATE-TIME:20240926T113000Z DTEND;VALUE=DATE-TIME:20240926T115000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-312@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleg Gerasymov (Odesa Mechnikov National University )\nThe study of the influence of local properties of multi-particle congl omerations on their macroscopic properties is one among of the traditional ly relevant problems of statistical physics. Parameterization of local pro perties can be carried out in various ways\, for example\, in terms of ord ering parameter tensors\, Euler invariants\, Voronoi tessellations and oth ers. While the macroscopic properties discussed above are the usual ones i n statistical physics and thermodynamics\, like compressibility\, heat cap acity\, thermal conductivity\, and others. In this paper\, we study the in fluence of the compaction factor (packing) on the property of compressibil ity using the example of a model conglomeration of solid spheres\, startin g with a mono-disperse system and further\, for multi-component mixtures. Using the known equations of state of the Carnahan-Starling type and their generalizations to the case of poly-disperse mixtures\, the inverse probl em of the influence of the proper parameters of the system (mixture) on th e degree of compaction (packing) is considered. Non-monotonicity in the be havior of the packing parameter and the possibility of achieving its maxim um value using a consistent selection of relations of the sizes of compone nts and their molar fractions are shown. Application of the above-describe d approach to two different physical systems - a binary liquid mixture and a two-component granular system - showed quite good agreement between the ory and experiment (especially in the case of a granular system). The prop osed approach can be generalized without fundamental difficulties to the c ase of multi-particle conglomerations with an arbitrary number of componen ts.\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/312/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/312/ END:VEVENT BEGIN:VEVENT SUMMARY:Polarization mechanism of bacteria motion in aquatic media DTSTART;VALUE=DATE-TIME:20240926T101000Z DTEND;VALUE=DATE-TIME:20240926T103000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-328@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksandr Cherniak (Bogolyubov Institute for Theoret ical Physics)\nA new mechanism is proposed to explain the reasons for the bacteria's motion in the aquatic environment. The mathematical model of th is mechanism is based on the hydrodynamic equations of active matter and t akes into account the dynamics of the environment polarization and polariz ation of individual bacteria. It is assumed that the flow of light and the active motion of dielectric regions with different refractive indices ins ide the bacterium lead to the formation of a nonuniform distribution of di pole moments at the interface between the bacterium and the aqueous medium . This distribution is nonequilibrium and evolves along the bacterium and rotates. The interaction of this distribution with the environment due to surface deformation or due to ponderomotive force leads to the bacteria's motion. Such a motion can be represented as a type of turbine effect witho ut attachment or as an interaction of the polarization current with a chan ge in the local polarization of the medium. This mechanism differs signifi cantly from the flagella motion mechanism and can explain the motility of flagellate bacteria. In addition\, such a mechanism depends on the concent ration of charged particles in the medium. Namely\, with an increase in th eir concentration\, the polarized region motion increases\, which creates a greater bacterial surface deformation and causes a redistribution of pol arization. Moreover\, the collective bacteria motion can cause water mixin g.\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/328/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/328/ END:VEVENT BEGIN:VEVENT SUMMARY:Kinetic model of the formation of STM-induced electrofluorochromis m in molecular junctions DTSTART;VALUE=DATE-TIME:20240926T095000Z DTEND;VALUE=DATE-TIME:20240926T101000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-333@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksiy Kapitanchuk (Bogolyubov Institute for Theore tical Physics\, National Academy of Sciences of Ukraine)\nExperimental dat a on STM-induced electroluminescence in monomolecular junctions have led t o the need to elucidate the physics of the formation of optoelectronic pro cesses at the atomic-molecular level\, taking into account both dynamic an d relaxation processes. A mechanism for the formation of electrofluorochro mism based on a kinetic model has been proposed [1]. In this model\, the d escription of the optoelectronic process in a photoactive molecular juncti on takes into account the fact that the formation of electron current and electroluminescence (EL) is controlled not only by the shift of the orbita l energies of the molecule relative to the Fermi levels of both electrodes \, but also by the probability of the realization of many-body states of t he molecule at different values and polarities of the bias voltage. Theref ore\, when current and EL are generated\, the electronic states of charged forms of fluorophore molecules can act not only as mediators of electron transfer\, but also become responsible for electrofluorochromism. It becam e clear that the EL in a molecular junction reflects the light emission of a fluorophore molecule not only between the singlet states of a neutral m olecule\, but also between the states of its charged forms. Thus\, we show that electron transfer occurs through the transmission channels associate d with electronic states of the neutral molecule and its cationic and anio nic forms\, which\, at a definite bias voltages\, are involved in electron transfer. The occupancies of these states are determined by kinetic proce sses in the molecular junction and therefore depend on the ratio of charg e exchange rates between the molecule and the electrodes\, the rates of no n-radiative intramolecular transitions caused by inelastic interelectrode tunneling of electrons\, as well as the rates of intramolecular radiative transitions enhanced by the plasmonic response. Analytical results are obt ained using the tight-binding Hamiltonian for a molecule. The kinetic mode l made it possible to explain the features of EL in a monomolecular juncti on with the ZnPc fluorophore. Thus\, it was shown that the description of EL based on the kinetic approach can serve as an effective tool for unders tanding the physics of optoelectronic processes in single-molecule structu res.\n\n1. E.Petrov\, O.Kapitanchuk\, Ye.Shevchenko\, V.Gorbach\, A.Lyubch ik\, Phys. Chem. Chem. Phys.\, 2024\, DOI: 10.1039/d4cp01328j\n\nhttps://i ndico.bitp.kiev.ua/event/13/contributions/333/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/333/ END:VEVENT BEGIN:VEVENT SUMMARY:Dynamics of correlations of many colliding particles DTSTART;VALUE=DATE-TIME:20240926T093000Z DTEND;VALUE=DATE-TIME:20240926T095000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-297@indico.bitp.kiev.ua DESCRIPTION:Speakers: Viktor Gerasimenko (Institute of Mathematics NAS of Ukraine)\nThe talk provides an overview of some advances in the mathematic al understanding of the nature of the dynamics of the correlations of many colliding particles. The fundamental equations of modern mathematical phy sics are studied\, in particular the hierarchies of the evolution equation s of many hard spheres and their asymptotic behavior described by kinetic nonlinear equations.\n\nFirst\, an approach to describing correlations in a system of colliding particles interacting as hard spheres is discussed\, based on a hierarchy of equations for the evolution of a sequence of corr elation functions that are cumulants of distribution functions\, called th e Lioville hierarchy. It is proven that the constructed dynamics of correl ations underlie the description of the dynamics of both a finite and an in finite number of hard spheres obeying the BBGKY hierarchies for reduced (m arginal) distribution functions or reduced correlation functions.\n\nThe s tructure of expansions representing non-perturbative solutions of the Cauc hy problem for these hierarchies of evolution equations is formulated. It has been established that the concept of cumulants of the groups of operat ors of the Lioville equations underlies non-perturbative expansions of sol utions to the hierarchies of fundamental equations describing the evolutio n of observables and of the state of many hard spheres\, as well as forms the basis of the kinetic description of their collective behavior.\n\nIn t he talk\, we also consider a new approach to the problem of a rigorous des cription of kinetic evolution by means of reduced (marginal) observables g overned by the dual BBGKY hierarchy. One of the advantages of the develope d approach to the derivation of kinetic equations from the underlying dyna mics of many particles is that it provides an opportunity to construct kin etic equations with initial correlations\, in particular correlations char acterizing the condensed states of a system\, and to describe the processe s of the propagation of initial correlations within suitable scaling limit s.\n\nReferences\n[1] Gerasimenko V I and Gapyak I V 2023 Advances in theo ry of evolution equations of many colliding particles. *Proc. Inst. Math. NASU* **20** 729–804 doi:10.3842/trim.v20n1.528\n[2] Gerasimenko V I and Gapyak I V 2022 Propagation of correlations in a hard sphere system. *J S tat. Phys.* **189** 2 doi:10.1007/s10955-022-02958-8\n[3] Gerasimenko V I and Gapyak I V 2021 Boltzmann–Grad asymptotic behavior of collisional dy namics. *Reviews in Math. Phys.* **33** 2130001 32 doi:10.1142/S0129055X21 300016\n[4] Gerasimenko V I and Gapyak I V 2019 Processes of creation and propagation\nof correlations in large quantum particle system. In: *Panora ma of Contemporary Quantum Mechanics – Concepts and Applications.* Londo n: InTech\, 2019 doi:10.5772/intechopen.82836\n\nhttps://indico.bitp.kiev. ua/event/13/contributions/297/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/297/ END:VEVENT BEGIN:VEVENT SUMMARY:Development and analysis of novel integrable nonlinear dynamical s ystems on quasi-one-dimensional lattices. Parametrically driven nonlinear system of pseudo-excitations on a two-leg ladder lattice DTSTART;VALUE=DATE-TIME:20240926T084000Z DTEND;VALUE=DATE-TIME:20240926T090000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-336@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksiy O. Vakhnenko (Bogolyubov Institute for Theor etical Physics)\nFollowing the main principles of developing the evolution ary nonlinear integrable systems on quasi-one-dimensional lattices we sugg est the novel nonlinear integrable system of parametrically driven pseudo- excitations on a regular two-leg ladder lattice. The initial (prototype) f orm of the system is derivable in the framework of semi-discrete zero-curv ature equation with the spectral and evolution operators specified by the properly organized 3×3 square matrices. Although the lowest conserved loc al densities found via the direct recursive method do not prompt us the al gebraic structure of system's Hamiltonian function\, but the heuristically substantiated search for the suitable two-stage transformation of prototy pe field functions to the physically motivated ones has allowed to disclos e the physically meaningful nonlinear integrable system with time-dependen t longitudinal and transverse inter-site coupling parameters. The time dep endencies of inter-site coupling parameters in the transformed system are consistently dened in terms of the accompanying parametric driver formaliz ed by the set of four homogeneous ordinary linear dierential equations wit h the time-dependent coeficients. The physically meaningful parametrically driven nonlinear system permits its concise Hamiltonian formulation with the two pairs of field functions serving as the two pairs of canonically c onjugated field amplitudes. The explicit example of oscillatory parametric drive is described in full mathematical details.\n\nhttps://indico.bitp.k iev.ua/event/13/contributions/336/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/336/ END:VEVENT BEGIN:VEVENT SUMMARY:Stimulating exitable membrane of ORN with stochastic Markov proces s DTSTART;VALUE=DATE-TIME:20240926T082000Z DTEND;VALUE=DATE-TIME:20240926T084000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-358@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksandr Vidybida (Bogolyubov Institute for Theoret ical Physics)\nExcitable membrane of olfactory receptor neuron (ORN) is po pulated with up to several millions of identical receptor proteins (R) abl e to bind / release odor (O) molecules. The affinity of R to O depends on the odor presented\, and this is the initial mechanism which is recuired f or the olfactory selectivity to exist.\n\n\nFigure 1: Simplified R structu re. Modified from [3].\n\nThe affinity of R to O depends on the odor prese nted\, and this is the very first step the olfactory selectivity builds up . Recently\, [1]\, it was shown for a so called membrane-less ORN model th at its selectivity can be much better than that of its R. A more realistic ORN model should include an excitable membrane with its electric transien ts. This introduces time parameter into the ORN's response to stimulation. The latter renders inappropriate used in [1] reasoning in terms of binomi al distribution\, and necessitates consideration of temporal properties of O binding-releasing and the membrane charging-discharging-firing.\n\nIn t his contribution\, we develop an approach in which the number of R bound w ith O $n(t)$\, is modeled as a Markov stochastic process. With each bound R\, \nas it is observed for insects [2]\, Fig. 1\, we associate an open ch annel having conductance 0.015 nS\, which injects a depolarizing current t hrough the membrane.\n The futher membrane evolution is governed by the le aky integrate-and-fire neuronal model\, see Eq. (1).\n$c_M\\frac{dV(t)}{dt }=-g_l(V(t)-V_{rest}) - n(t)g_{R}(V(t)-V_{e})$\,\nwhere $V(t)$ --- is the membrane voltage\; $V_{rest}$ --- is the resting voltage\;\n$c_M$ --- is t he total capacity of ORN's membrane\;\n$g_l$ --- is the total leakage thro ugh it\;\n$V_{e}$ --- is the reversal potential for current through open $ R$\;\n$n(t)$ --- is the fluctuating number of open channels at moment $t$ due\nto odor molecules bound with $R$s\;\n$g_{R}$ --- is the conductance o f a single open channel.\n\nA fast\, very efficient method is developed fo r generating stochastic trajectories $n(t)$ and solving Eq. (1) numericall y\, see Fig. 2. The first\, introductory simulations based on this method\ , [4]\, support the conclusion made in [1] and before\, that ORN's selecti vity can be much better than that of its receptors R\, provided that odors are presented in low concentrations.\n\n\nFigure 2: An example of realiza tion of stochastic process n(t) and corresponding membrane voltage\, with three spikes emitted. Here\, the total number of R per the ORN is $N = 2.5 · 10^6$\n\n[1] A. K. Vidybida\, ``Maximization of the olfactory receptor neuron selectivity in\n the sub-threshold regime''\, Ukrainian Journal o f Physics\, vol. 68\, no.4\, p. 266\, 2023. Available: {\\tt https://doi.o rg/10.15407/ujpe68.4.266}\n\n[2] K. Sato\, M. Pellegrino\, T. Nakagawa\, T . Nakagawa\, L. B. Vosshall\, and\n K. Touhara\, ``Insect olfactory recep tors are heteromeric ligand-gated ion\n channels''\, Nature\, vol. 452\, no. 7190\, pp. 1002--1006\, 2008. Available: {\\tt https://doi.org/10.1038 /nature06850}\n\n[3] D. Wicher\, F. Miazzi\, ``Functional properties of in sect olfactory receptors: ionotropic receptors and odorant receptors''\, C ell and Tissue Research\, vol. 383(1):7-19 (2021). Available: {\\tt https: //doi.org/10.1007/s00441-020-03363-x}\n\n[4] A. Vidybida\, "Selectivity Ga in in Olfactory Receptor Neuron at Optimal Odor Concentration\," 2024 IEEE International Symposium on Olfaction and Electronic Nose (ISOEN)\, Grapev ine\, TX\, USA\, 2024\, pp. 1-3. Available: {\\tt https://ieeexplore.ieee. org/document/10556323}\n\nhttps://indico.bitp.kiev.ua/event/13/contributio ns/358/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/358/ END:VEVENT BEGIN:VEVENT SUMMARY:Recursive Method for Calculating T-Matrix of Electron Scattering o n Arbitrary Many-Particle Clusters in Strongly Correlated Systems DTSTART;VALUE=DATE-TIME:20240926T080000Z DTEND;VALUE=DATE-TIME:20240926T082000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-347@indico.bitp.kiev.ua DESCRIPTION:Speakers: Tatiana Shatnii (G. V. Kurdyumov Institute for Metal Physics\, N.A.S. of Ukraine)\nThe generalized recursive method for calcul ating the T-matrix of electron scattering on arbitrary many-particle clust ers for determining the Green's function of the strongly correlated system is developed. This approach is extended to the studying electronic spectr a in both direct (Wannier) and reciprocal (Bloch) representations with tak ing into account the influence of atomic and magnetic correlations arising in the system at a temperature of 0 K. The one-band Hubbard model\, the c orrelated random field approximation\, and the one-site coherent potential approximation for the effective Hamiltonian of system are also used in th is approach. The spectral density in reciprocal space is calculated in the same way (the same scheme) as in direct space\, using the appropriate exp ressions for the effective Green's function\, which includes contributions from all crystal sublattices. Calculation of the small parameter of the c luster expansion of the Green's function in direct and reciprocal represen tations shows its smallness for different parameters of b.c.c alloys. This ensures the convergence of obtained recursive formulas for T-matrix of sc attering on many-particle clusters and the applicability of pairwise appro ximation for T-matrix. It should be noted that to calculate the configurat ion-averaged Green's function it is necessary to use at least the pairwise approximation of T-matrix for describing the influence of the cluster env ironment of each atom on the redistribution of charge and spin densities o n atoms\, as well as atomic and magnetic correlations. In addition\, the p ossibility of nanoclusters formation and their influence on the magnetic s tate was investigated in the b.c.c. alloy with strong electron correlation s. The calculation of electronic spectra in the reciprocal (as in direct) representation showed the high sensitivity to the changes in the character istics and composition of the b.c.c. alloy including the nanoclusters form ation as well as to the change of resulting short-range atomic and magneti c orders. This method could be useful to analyze experimental data obtaine d\, for example\, in positron spectroscopy to study electronic structure\, defects\, chemical composition\, and various correlations in systems.\n** Key words:** Green's function for strongly correlated alloys\, recursive e xpression for T-matrix\, arbitrary many-particle clusters\, short-range at omic and magnetic ordering.\n\nhttps://indico.bitp.kiev.ua/event/13/contri butions/347/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/347/ END:VEVENT BEGIN:VEVENT SUMMARY:Impurity-induced localized modes in parallel Josephson junction ar rays DTSTART;VALUE=DATE-TIME:20240926T074000Z DTEND;VALUE=DATE-TIME:20240926T080000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-350@indico.bitp.kiev.ua DESCRIPTION:Speakers: Daryna Bukatova (Bogolyubov Institute for Theoretica l Physics)\nWe consider inhomogeneous underdamped one-dimensional parallel Josephson junction arrays. Inhomogeneity is introduced either as a non-un iformly applied dc bias current or as variations in the junctions' critica l currents. We investigate the frequency of the localized modes induced by the presence of such inhomogeneities\, in particular the frequency's depe ndence on the parameters that characterise inhomogeneities.\n\nhttps://ind ico.bitp.kiev.ua/event/13/contributions/350/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/350/ END:VEVENT BEGIN:VEVENT SUMMARY:Sagnac effect in solids DTSTART;VALUE=DATE-TIME:20240926T072000Z DTEND;VALUE=DATE-TIME:20240926T074000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-310@indico.bitp.kiev.ua DESCRIPTION:Speakers: Sergei Sharapov (Bogolyubov Institute for Theoretica l Physics of the National Academy of Sciences of Ukraine Kyiv Academic University)\nThe observation of the Sagnac effect for massive material par ticles offers a significant enhancement in sensitivity when compared to op tical interferometers with equal area and angular rotation velocity. For t his reason\, there have been suggestions to employ solid-state interferome ters that rely on semiconductors and graphene. We investigate the Sagnac e ffect in Dirac materials governed by the relativistic-like quasiparticle d ispersion law and show that the fringe shift is still determined by the ma ss of a free electron. This confirms that graphene is indeed a promising m aterial for creating solid-state Sagnac interferometers. Considering monol ayer graphene with its linear dispersion law and comparing it with light p rovides a deeper understanding of the Sagnac effect.\n\nhttps://indico.bit p.kiev.ua/event/13/contributions/310/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/310/ END:VEVENT BEGIN:VEVENT SUMMARY:Analytical Description of Size Effects\, Strains and Ferro-ionic C oupling in Si-Compatible Nanosized Ferroelectrics DTSTART;VALUE=DATE-TIME:20240926T070000Z DTEND;VALUE=DATE-TIME:20240926T072000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-331@indico.bitp.kiev.ua DESCRIPTION:Speakers: Anna Morozovska (Institute of Physics\, National Aca demy of Sciences of Ukraine)\nThe analytical methods based on the Landau-G inzburg-Devonshire (LGD) approach and variational principle allow the anal ytical description of size effects\, strain and ferro-ionic coupling in lo w-dimensional ferroelectric materials\, such as thin films and small nanop articles. The validity of LGD approach is corroborated by experimental evi dence of the size- and strain-induced transitions as well as the related p henomena in the low-dimensional ferroelectric materials. For the correct d escription of these effects in ferroelectric thin films and small nanopart icles the LGD approach should be combined with the classical electrostatic s and elasticity theory\, and variational principle. It is important to de termine how the LGD expansion coefficients depend on various factors\, suc h as temperature\, size\, elastic stresses and/or strains\, and ionic-elec tronic charge density and distribution. For classical ferroelectric films with a pronounced temperature-dependent and strain-dependent soft mode\, t he first expansion coefficients have a linear dependence on the temperatur e and elastic strain.\nThe significant attention is devoted to the compari son with experimental results and finite element modelling\, as well as on the theoretical predictions of the size-\, strain- and ionic- control of polar and dielectric properties of nanosized ferroelectric materials.\nAs the first example\, we consider ultra-thin layers and nanoflakes of van de r Waals ferrielectric CuInP2S6 covered by an ionic surface charge and reve al the appearance of polar states with relatively high polarization and st ored free charge\, which can mimic “mid-gap” states related with a sur face field-induced transfer of Cu and/or In ions in the van der Waals gap [1]. The changes of the ionic screening degree and mismatch strains can in duce the transitions between paraelectric phase\, antiferroelectric\, ferr ielectric\, and ferroelectric-like states in CuInP2S6 nanoflakes. Due to t he emergence of manyfold-degenerated metastable states of spontaneous pola rization the ultra-thin layers of CuInP2S6 reveal features of the controll able negative capacitance effect [2]\, which make them attractive for adva nced electronic devices\, such as nano-capacitors and gate oxide nanomater ials with reduced heat dissipation.\nAs the second example\, we use the LG D model to quantify the strain-charge-polarization coupling in nanosized H fxZr1-xO2. A key factor ruling the observed polar properties of nanosized HfxZr1-xO2 is the presence of the polar orthorhombic phase. This phase is metastabile compared to the bulk monoclinic phase\, leading to problems wi th the ferroelectric phase stability in nanoscale. The electrophysical pro perties of the HfxZr1-xO2 thin films and nanoparticles are very sensitive to the elastic strain induced by the substrate\, annealing conditions\, de position method\, film thickness\, content x and dopants. Depending on the interplay of these factors\, the nanosized HfxZr1-xO2 exhibits dielectric \, ferroelectric\, or antiferroelectric behavior. \nThe used model [3] inc orporates parametrized Landau expansion coefficients for the polar and ant ipolar orderings. Obtained results agrees with the recent existing experim ental data for HfxZr1-xO2-y thin films and oxygen-deficient HfO2-y nanopar ticles [4]\, namely the X-ray diffraction confirmed the formation of a fer roelectric orthorhombic phase in the HfO2-y nanoparticles under special fa vorable annealing conditions. \nThe analytical LGD approach correctly pred icts the phase diagrams\, ground and metastable states\, alongside the dom ain structure morphology\, associated polar and structural properties of H fxZr1-xO2-y thin films and nanoparticles with different shapes and sizes. The successful application of the analytical LGD approach can be useful fo r the prediction of the silicon-compatible ferroelectric nanomaterials bas ed on HfxZr1-xO2-y. \nThe work is funded by the National Research Foundati on of Ukraine (projects “Manyfold-degenerated metastable states of spont aneous polarization in nanoferroics: theory\, experiment and perspectives for digital nanoelectronics”\, grant N 2023.03/0132 and “Silicon-compa tible ferroelectric nanocomposites for electronics and sensors”\, grant N 2023.03/0127).\n[1]. Anna N. Morozovska\, Sergei V. Kalinin\, Eugene A. Eliseev\, Svitlana Kopyl\, Yulian M. Vysochanskii\, and Dean R. Evans. Fer ri-ionic Coupling in CuInP2S6 Nanoflakes: Polarization States and Controll able Negative Capacitance (2024)\, https://doi.org/10.48550/arXiv.2405.143 68\n[2]. Anna N. Morozovska\, Eugene A. Eliseev\, Yulian M. Vysochanskii\, Sergei V. Kalinin\, and Maksym V. Strikha. Size Effect of Negative Capaci tance State and Subthreshold Swing in Van der Waals Ferrielectric Field-Ef fect Transistors\, https://doi.org/10.48550/arXiv.2406.13051\n[3]. Anna N. Morozovska\, Maksym V. Strikha\, Kyle P. Kelley\, Sergei V. Kalinin\, and Eugene A. Eliseev. Effective Landau-type model of a HfxZr1-xO2-graphene n anostructure\, Phys. Rev. Applied 20\, 054007 (2023) https://doi.org/10.11 03/PhysRevApplied.20.054007\n[4]. Eugene A. Eliseev\, Yuri O. Zagorodniy\, Victor N. Pavlikov\, Oksana V. Leshchenko\, Hanna V. Shevilakova\, Mirosl av V. Karpec\, Andrei D. Yaremkevych\, Olena M. Fesenko\, Sergei V. Kalini n\, and Anna N. Morozovska. Phase diagrams and polarization reversal in na nosized HfxZr1-xO2-y\, AIP Advances\, 14\, 055224 (2024)\, https://doi.org /10.1063/5.0209123\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/3 31/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/331/ END:VEVENT BEGIN:VEVENT SUMMARY:Chemical freeze-out curve in heavy-ion collisions and the QCD crit ical point DTSTART;VALUE=DATE-TIME:20240925T134000Z DTEND;VALUE=DATE-TIME:20240925T140000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-316@indico.bitp.kiev.ua DESCRIPTION:Speakers: Artemiy Lysenko (Bogolyubov Institute of Theoretical Physics)\nThe chemical freeze-out curve in heavy-ion collisions is invest igated in the context of QCD critical point (CP) search at finite baryon d ensities. Taking the hadron resonance gas picture at face value\, chemical freeze-out points at a given baryochemical potential provide a lower boun d on the possible temperature of the QCD CP. We first verify that the free ze-out data in heavy-ion collisions are well described by a constant energ y per particle curve\, $E/N = \\rm const$\, under strangeness neutrality c onditions ($\\mu_S \\neq 0$\, $\\mu_Q \\neq 0$). We then evaluate the hypo thetical freeze-out curve based on this criterion in the absence of strang eness neutrality ($\\mu_S = 0$\, $\\mu_Q = 0$) and confront it with recent predictions on the CP location. We find that recent estimates based on Ya ng-Lee edge singularities from lattice QCD data on coarse lattices place t he CP significantly below the freeze-out curve and are thus disfavored by the heavy-ion data. On the other hand\, predictions based on functional me thods and holography place the CP slightly above the freeze-out curve\, in dicating that the QCD CP may be located very close to the chemical freeze- out in A+A collisions at $\\sqrt{s_{NN}} = 3.5\\div5$ GeV. \n\nThe report is based on a recently published article: https://arxiv.org/abs/2408.06473 \n\nhttps://indico.bitp.kiev.ua/event/13/contributions/316/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/316/ END:VEVENT BEGIN:VEVENT SUMMARY:Four types of phase transitions in interacting boson system at hig h temperatures DTSTART;VALUE=DATE-TIME:20240925T132000Z DTEND;VALUE=DATE-TIME:20240925T134000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-340@indico.bitp.kiev.ua DESCRIPTION:Speakers: Dmytro Anchyshkin (Bogolyubov Institute for Theoreti cal Physics of the National Academy of Sciences of Ukraine\, FIAS)\nWithin the framework of the mean-field model\, the thermodynamics of the relativ istic bosonic system of interacting particles and antiparticles in the pre sence of a Bose-Einstein condensate is investigated. It is assumed that th e total isospin (charge) density is conserved. It is shown that the partic le-antiparticle boson system reveals four types of phase transitions into the condensate phase. Three types belong to the phase transition of the se cond order and one to the first order. We show that the grand canonical en semble is not suitable for describing a bosonic system of particles and an tiparticles in the presence of condensate\, but an adequate study can be c arried out within the framework of the canonical ensemble\, where the chem ical potential is a thermodynamic quantity that depends on the canonical f ree variables.\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/340/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/340/ END:VEVENT BEGIN:VEVENT SUMMARY:Application of Langevin dynamics for optimization in machine learn ing tasks DTSTART;VALUE=DATE-TIME:20240925T123000Z DTEND;VALUE=DATE-TIME:20240925T125000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-314@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksandr Borysenko (National Science Center "Kharki v Institute of Physics and Technology'")\nA rapid growth of Machine Learni ng (ML) applications in different areas has been faced in recent years. Tr aining of ML models is performed by finding such values of their parameter s $x=\\{x_1\, x_2\, ...\, x_N\\}$ that optimize (minimize) the objective (loss) function $U(x)$. Usually\, the number of parameters $N$ is large an d the training dataset is massive. Therefore\, to reduce computational cos ts\, the gradient $f=-dU(x)/dx$ of the objective function with respect t o the model parameters is computed on relatively small subsets of the trai ning data\, called mini-batches. If these mini-batches are selected random ly from the training dataset\, then the estimated values of the loss $\\ha t{U}(x)$ and its gradient $\\hat{f}=-d\\hat{U}(x)/dx$ are the stochastic approximations of their exact values. Therefore\, it is natural to apply L angevin dynamics to treat this stochastic optimization problem. We conside r the next discrete form of the Langevin equation:\n\n $\\frac{\\Delta x_{ n+1} - \\Delta x_{n}}{\\Delta t^{2}} = \\hat{f}_{n} - \\gamma \\frac{\\Del ta x_{n+1} + \\Delta x_{n}}{2 \\Delta t}\,$ (1)\n\n\n where $n$ is an iteration number\, $\\Delta x_{n+1} = x_{n+1} - x_{n}$\, $\\Delta t$ is a time step and $\\gamma>0$ is a viscous friction coefficie nt.\nNow\, it is straightforward to obtain the next parameter updating for mula:\n\n$\\Delta x_{n+1} = \\rho \\Delta x_{n} + \\hat{f}_{n} \\cdot \\et a\,$ (2) \n\n\nwhere $\\rho = (1-\\gamma \\Delta t /2)/(1+\\gamma \\Delt a t /2)$ is conventionally called a momentum coefficient and $\\eta = \\De lta t^{2}(1+\\rho)/2$ a learning rate constant.\nEquation (2) was derived in our recent work where we have introduced Coolmomentum – a method for stochastic optimization by Langevin dynamics with simulated annealing [1]. To implement simulated annealing (or slow cooling\, in physical terms)\, we apply a certain schedule for the gradual momentum coefficient decrease in the range\n\n$0 \\leq \\rho \n\nhttps://indico.bitp.kiev.ua/event/13/co ntributions/314/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/314/ END:VEVENT BEGIN:VEVENT SUMMARY:Resetting random walks in a bounded chain DTSTART;VALUE=DATE-TIME:20240925T121000Z DTEND;VALUE=DATE-TIME:20240925T123000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-326@indico.bitp.kiev.ua DESCRIPTION:Speakers: Leonid Christophorov (Bogolyubov Institute for Theor etical Physics\, NAS Ukraine)\nThe search of a target of unknown location is often random and ineffective\, especially when the search domain is spa cious and there is a lot of detrimental trajectories. To get rid of them\, thereby improving the search\, interruptions of the latter with starting it from scratch can be a good strategy. Called resetting\, such a manner i s in fact inherent to many search processes at very diverse levels of orga nization.\n Initiated by the seminal work [1] devoted to diffusion with re setting along an infinite chain\, the study of resetting effects in variou s model systems has quickly become a flourishing branch of the theory of s tochastic processes. The vast majority of corresponding works\, however\, concerns spatially continuous models\, whereas their discrete counterparts ‒ such as random walks in lattices or networks ‒ are not less importa nt. For the latter\, there were practically no exact results even in one d imension.\n In the present talk\, the recent results [2] on the resetting effects in one of the basic model ‒ classical random walks with Poissoni an resetting in a one-dimensional lattice ‒ are expounded at length. The model is analyzed in its general version\, for arbitrary initial and boun dary conditions\, which lead to a variety of optimization scenarios illust rated by non-standard behavior of the main observables (splitting probabil ities\, mean first passage times\, coefficients of variation). A quantum a nalog of the model is briefly discussed.\n\n1. M.R. Evans\, S.N. Majumdar. Phys. Rev. Lett. 106\, 160601 (2011).\n2. L.N. Christophorov. Rep. Natl. Acad. Sci. Ukraine (Dopovidi) 8\, 43 (2020)\; J. Phys. A: Math. Theor. 54\ , 015001 (2021)\; J. Phys. A: Math. Theor. 55\, 155006 (2022)\; Ukr. J. Ph ys. (2024).\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/326/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/326/ END:VEVENT BEGIN:VEVENT SUMMARY:Effect of the photon subsystem on the magnetic properties of quant um gases in equilibrium with radiation DTSTART;VALUE=DATE-TIME:20240925T113000Z DTEND;VALUE=DATE-TIME:20240925T121000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-349@indico.bitp.kiev.ua DESCRIPTION:Speakers: Юрій Слюсаренко (Інститут те оретичної фізики імені О.І. Ахієзера\, На ціональний науковий центр "Харківський фізико-технічний інститут"\, НАН України\ ; Харківський національний університет імені В.Н. Каразіна\; Національний універ ситет «Львівська політехніка»)\nWe study the im pact of the photon subsystem on the magnetic properties of a mixture of qu antum gases in thermodynamic equilibrium with it. Having proposed a simple model of the system\, we obtain general equations describing the thermody namic equilibrium of quantum gases of two-level atoms with photons. The re sulting equations are solved at a temperature higher than the degeneracy t emperature of all three components. The analysis of the solutions shows th e non-trivial dependence of magnetic properties on photon density and inte nsity of the external magnetic field. An increase in photon density due to external sources can lead to an increase in both magnetization and densit y of excited atoms. Such a conclusion is not a priori trivial since a phot on in a vacuum does not have a magnetic moment.\n\n*The authors acknowledg e support by the National Research Foundation of Ukraine under the call “Excellence Science in Ukraine”\, project No. 235/0073.*\n\nhttps://in dico.bitp.kiev.ua/event/13/contributions/349/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/349/ END:VEVENT BEGIN:VEVENT SUMMARY:Modeling temperature dynamics in non-uniform biological tissues un der cryogenic impact DTSTART;VALUE=DATE-TIME:20240925T101000Z DTEND;VALUE=DATE-TIME:20240925T103000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-364@indico.bitp.kiev.ua DESCRIPTION:Speakers: Sergey Shevchenko (B. Verkin ILTPE of NASU)\nPhysica l and mathematical modeling is widely used to simulate cryoapplication pro cesses. Mathematical modeling of this process [1\,2] allows us to predict the temperature field of the frozen region. This makes it possible to dete rmine the cryo-application time sufficient to destroy target cells and min imize damage to healthy cells under various experimental conditions. Moreo ver\, simulation also predicts the depth of the cryoapplication impact\, w hich can be difficult to measure in some situations in the living tissues. Then\, we use temperature-dependent thermodynamical parameters of biologi cal tissues to compare simulation with thermal imaging.\nThe problem with moving phase boundary is known as the Stefan problem. There are several wa ys to numerically solve that problem. One of them is gradually changing th ermodynamic parameters close to the phase change boundary. This approach i s effectively describing the freezing dynamics of a biological tissues. Th e appearance of solutes in water leads to change the freezing temperature in a range of temperatures around (-10C..-0.1C) due to change of solute co ncentration. By combining the usual thermal capacity with latent heat\, we can define an effective thermal capacity. That allows us to solve the hea t equation in 2D cylindrical geometry\, see Fig. 1.\n Generally thermodyna mic properties of the biological tissues are highly dependent on temperatu re\, so we have a non-uniform heat equation $\\frac{\\partial T}{\\partial t}=\\frac{1}{\\rho C_\\text{p}}\\nabla k\\nabla T$ . To solve this equati on numerically\, we use the finite differences method on a rectangular mes h to calculate the thermal balance of each node. Then we compare our resul ts with thermal imaging of cryoapplication impact on rat skin [3].\n\n\n\n Fig. 1. (a) Principal scheme of the cryo-application problem for 2D cylind rical geometry with radial symmetry\, where there is the cryo-applicator w ith a temperature of liquid Nitrogen pressed 1-2mm inside the soft tissues . (b) Dynamics of the maximum radius and depth of the ice spot for several isotherms. Typically consists of 4 phases\, I-freezing\, II-thawing thin layer of ice around the main ice spot\, III-usual thawing\, IV-finish thaw ing.\nAcknowledgments: This research is sponsored by the National Research Foundation of Ukraine (Grant No. 2022.01/0094).\n[1] M. Rossi and Y. Rabi n\, in: Proc. Int. Conf. "Modeling\, Simulation & Visualization Methods" ( MSV 2007)\, CSREA Press\, 187-193.\n[2] Y. Rabin and A. Shitzer\, J. Biome ch. Eng.\, 1997\, 119\, 146-152. \n[3] G. Kovalev et al.\, Problems of Cry obiology and Cryomedicine\, 2020 30\, 359-368\n\nhttps://indico.bitp.kiev. ua/event/13/contributions/364/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/364/ END:VEVENT BEGIN:VEVENT SUMMARY:Domains and domain boundaries structure of benzene adsorbed on gra phene DTSTART;VALUE=DATE-TIME:20240925T095000Z DTEND;VALUE=DATE-TIME:20240925T101000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-354@indico.bitp.kiev.ua DESCRIPTION:Speakers: Yevhenii Trotskyi (B. Verkin Institute for Low Tempe rature Physics and Engineering of the National Academy of Sciences of Ukra ine)\nIn our report\, we review the domain boundaries in the structure of benzene monolayer adsorbed on a graphene sheet. It is shown in [1] that th e monolayer’s structure can be complicated even for benzene\, the simple st representative of the cyclic hydrocarbons. It was found in [2] that the re exist two different energy states of the adsorbed benzene molecule: 1) the symmetric (hollow) unstable state\, where the benzene molecule is plac ed right over the graphene hexagon\; 2) the non-symmetric (stacked) stable configuration\, where the benzene molecule’s center is placed above one of graphene atoms. The low-symmetry structure is characterized by the pre sence of six domains\, known as star domains. The representatives of these domains at the graphene hexagonal layer are star vectors that describe tr ansitions from symmetric high energy state into the stable low symmetric p osition.\n\n\n[1]. Lykah\, V. A.\, & Syrkin\, E. S. (2022). Domains of the adsorbed benzene monolayer on graphene. Low Temperature Physics\, 48(4)\, 353-358.\nhttps://doi.org/10.1063/10.0009743\n\n[2]. Alzahrani\, A. Z. (2 011). Structural and electronic properties of graphene upon molecular adso rption: DFT comparative analysis. Graphene Simulation\, 1\, 21–38.\nhttp s://doi.org/10.5772/20356\n\nhttps://indico.bitp.kiev.ua/event/13/contribu tions/354/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/354/ END:VEVENT BEGIN:VEVENT SUMMARY:Squeezing and amplification in open quantum systems with color cen ters using the multilevel Janes-Cummings model DTSTART;VALUE=DATE-TIME:20240925T093000Z DTEND;VALUE=DATE-TIME:20240925T095000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-363@indico.bitp.kiev.ua DESCRIPTION:Speakers: Roman Ovsiannikov (NSC «Kharkov Institute of Physic s and Technology»)\nThe ability to couple cavity-confined microwave modes to diamond slabs or films containing large numbers of color centers opens up potential new methods for noise reduction\, processing\, and even gene rating quantum states of microwaves. The unique feature of various diamond color centers is that they can be prepared in their ground states by illu minating them with light in the optical band. The color centers then becom e a very low noise (effectively very low temperature) system for processin g and manipulating microwaves.\nEnsembles of few-level emitters are able t o generate nonlinearities for electromagnetic fields. Often\, this is done by arranging the level structure and driving to simultaneously induce the electromagnetically induced transparency to eliminate most of the absorpt ion that can accompany nonlinearities due to the decay of the emitter ener gy levels. For color centers\, the lowest lying spin levels\, e.g.\, three levels for nitrogen-vacancy (NV) centers\, have very long lifetimes\, so this is not a significant issue. Ensembles of emitters will also generate nonlinearities for single modes\, but the produced nonlinearities are limi ted to the maximal ones that can be generated by single emitters. Essentia lly\, for the purpose of generating nonlinearities\, having an ensemble ef fectively increases the coupling rate: if the coupling of each emitter is $g_0$\, then an ensemble with $N$ emitters acts as a single emitter with a coupling rate $g =\\sqrt{N}g_0$\, which is valid for the off-resonant gen eration of nonlinearities.\nAn ensemble of two-level emitters off-resonant with a single mode generates a series of nonlinearities with effective Ha miltonians given by powers of the mode energy operator $a^\\dagger a$. The first term in this series generates a frequency shift for the cavity mode proportional to ${g^2}/{\\Delta} $\, where $\\Delta$ is a detuning betwee n the NV-centers and the cavity mode. Modulating the frequency of a mode i nduces parametric amplification.\nIn this study we investigate the optimal modes of operation of a $N$-level atomic system interacting with the cavi ty mode to obtain squeezed states and amplification of the electromagnetic cavity mode signal. This is performed in the framework of the Janes-Cummi ngs model for the $N$-level atomic system within the rotating wave approxi mation. For this purpose\, perturbation theory\, namely the Magnus expansi on for the evolution operator\, up to and including second order of smalln ess\, was used.\nR.O. and A.S. acknowledge support by the National Researc h Foundation of Ukraine under the call "Excellent Science in Ukraine"\, pr oject No. 235/0073.\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/ 363/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/363/ END:VEVENT BEGIN:VEVENT SUMMARY:Thermodynamics of the kagome Heisenberg antiferromagnets DTSTART;VALUE=DATE-TIME:20240925T084000Z DTEND;VALUE=DATE-TIME:20240925T090000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-319@indico.bitp.kiev.ua DESCRIPTION:Speakers: Taras Hutak (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine)\nKagome-lattice Heisenberg antiferromagnet is a paradigmatic model in the field of frustrated magnet ism that allows us to study the interplay of geometrical frustration and q uantum as well as thermal fluctuations in two and three dimensions. Distin ctive spectrum of this model manifest itself in the thermodynamic properti es throughout the peculiar low-temperature behavior of the specific heat. \n\nWe use 16 terms of a high-temperature series expansion complemented by the entropy-method interpolation to examine the specific heat and the uni form susceptibility of the Heisenberg model on the three-dimensional kagom e (hyperkagome) lattice. We obtain thermodynamic quantities for several sc enarios determined by the behavior of the specific heat as the temperature tends to zero. All scenarios give rise to a low-temperature peak in $c(T) $ well below the main high-temperature peak. The functional form of the un iform susceptibility $\\chi(T)$ below about $T=0.5$ depends strongly on th e chosen scenario. An estimate for the ground-state energy $e_0$ depends o n the adopted specific scenario but is expected to lie between $−0.441$ and $−0.435$. In addition to the entropy-method interpolation\, we use t he finite-temperature Lanczos method to calculate $c(T)$ and $\\chi(T)$ fo r finite lattices of $N=24$ and $36$ sites.\n\nThis project is funded by t he National Research Foundation of Ukraine (2023.03/0063\, Frustrated quan tum magnets under various external conditions).\n\nhttps://indico.bitp.kie v.ua/event/13/contributions/319/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/319/ END:VEVENT BEGIN:VEVENT SUMMARY:Critical Behavior of Structurally Disordered Systems Magnets with Long-Range Interaction DTSTART;VALUE=DATE-TIME:20240925T082000Z DTEND;VALUE=DATE-TIME:20240925T084000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-335@indico.bitp.kiev.ua DESCRIPTION:Speakers: Dmytro Shapoval (Institute for Condensed Matter Phys ics of the National Academy of Sciences of Ukraine\; L4 Collaboration & Do ctoral College for the Statistical Physics of Complex Systems\, Leipzig-L orraine-Lviv-Coventry\, Europe)\nOur research aims to examine critical beh avior of a magnetic system under the influence of two competing factors: l ong-range interaction and weak structural disorder (e.g.\, weak quenched d ilution). We analyze ferromagnetic ordering in a structurally-disordered m agnet within an $n$-vector model in $d$-dimensional space\, where the long -range interaction decays with distance $x$ as $J(x) \\sim x^{-d -\\sigma} $\, where with $\\sigma$ as is the control parameter. Field-theoretical re normalization group methods (RG) are used to identify the system’s unive rsality classes\, and the universal characteristics of critical behavior d epending on the global parameters $d\, n\, \\sigma$. We demonstrate that there exists a parameter region $(d\, n\, \\sigma)$\, where the interplay of long-range interaction and structural disorder leads to emergence of a new structural-disorder-induced long-range universality class. Using fixed spatial dimension approach we extract values of correlation length critic al exponent $\\nu$ characterizing this class from perturbative RG function s at $d = 3$ applying asymptotic series resummation methods.\n\nThis work was supported by the National Research Foundation of Ukraine\, Project 246 /0099 "Criticality of complex systems: fundamental aspects and applicatio ns" .\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/335/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/335/ END:VEVENT BEGIN:VEVENT SUMMARY:Quantum topological effects in magnetization dynamics: the Berry p hase\, the Aharonov–Casher effect and electric field control of spin wav es dynamics DTSTART;VALUE=DATE-TIME:20240925T074000Z DTEND;VALUE=DATE-TIME:20240925T082000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-307@indico.bitp.kiev.ua DESCRIPTION:Speakers: Volodymyr Kryvoruchko (Donetsk Physics & Technology Institute named after O. O. Galkin\, NAS of Ukraine\, 46\, Nauki Avenue\, 03028 Kyiv)\nCondensed matter physics is revolutionizing by introducing to pology-based concepts that characterize a system's physical states and pro perties. An example of topological effects in magnetization dynamics is th e additional quantum mechanical phase\, the so-called Berry phase [1]\, an d the Aharonov–Casher (AC) effect [2]\, acquired by the quantum orbital motion of chargeless bosonic quasiparticles with magnetic dipole moment – e.g.\, spin waves (SWs) with magnetic moment µm = ±gµB – in mesos copic rings in an external electric (E) field. It manifests itself in a sh ift of the dispersion and the group velocity direction of SW by the E fiel d. In the linear approximation concerning the electric field\, the magnoni c AC effect can be considered by adding the Dzyaloshinskii-Moriya-like int eraction between neighboring spins. This topological quantum phenomenon ha s been directly detected experimentally for SWs propagating in the classic al magnetic insulator Y3Fe5O12 [3\,4]. The magnitude of the AC phase was t wo orders larger than previously estimated theoretically for centrosymmetr ic ferromagnet insulators. This finding allows for tuning the properties o f SWs\, an essential ingredient for magnonic devices\, by the E-field. Thr ough analytical calculations and micromagnetic simulations\, we demonstrat ed that in ferromagnetic\, antiferromagnetic\, and ferrimagnetic nanoscale films\, it is possible to control the SWs characteristics using an extern al E-field [5-9]. From the fundamental point of view\, the discussed quant um phenomena open a new avenue for quantifying topological effects in magn etization dynamics. The E-field control of SW dynamics in magnetic film ca n also be helpful for the development and designing of new magnonic nanode vices and could be utilized for quantum technologies. \nV.N.K. acknowledge s the financial support by the STCU\, project “Magnetism in Ukraine Init iative”\, project Agreement No. 9918. \n\n[1] M. V. Berry. Quantum phase factors accompanying adiabatic changes. Proc. R. Soc. London\, Ser. A 392 \, 45 (1984).\n[2] Y. Aharonov\, A. Casher. Topological quantum effects fo r neutral particles. Phys. Rev. Lett. 53\, 319 (1984).\n[3] X. Zhang\, T. Liu\, M. E. Flatté\, H. X. Tang. Electric field coupling to spin waves in a centrosymmetric ferrite. Phys. Rev. Lett. 113\, 037202 (2014).\n[4] R. O. Serha\, V. I. Vasyuchka\, A. A. Serga\, B. Hillebrands. Towards an expe rimental proof of the magnonic Aharonov-Casher effect. Phys. Rev. B 108\, L220404 (2023).\n[5] V. N. Krivoruchko\, A.S. Savchenko\, V. V. Kruglyak. Electric-field control of spin-wave power flow and caustics in thin magnet ic films. Phys. Rev. B 98\, 024427 (2018).\n[6] V. N. Krivoruchko\, A.S. S avchenko. Electric-field control of nonreciprocity of spin wave excitation in ferromagnetic nanostripes. J. Magn. Magn. Mater. 474\, 9 (2019). \n[7] V. N. Krivoruchko. Aharonov–Casher effect and electric field control of magnetization dynamics. Low Temp. Phys. 46\, 820 (2020).\n[8] O. Boliasov a\, V. Krivoruchko. Electric-Field Control of Magnetization Dynamics in An tiferromagnets. 2023 IEEE Nanotechnology Materials and Devices Conference (NMDC)\, Paestum (Salerno)\, Italy\; DOI:10.1109/NMDC57951.2023.10343910\n [9] V. N. Krivoruchko\, A.S. Savchenko. Controlled refraction and focusing of spin waves determined by the Aharonov-Casher effect. Phys. Rev. B 109\ , 184437 (2024).\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/307 / LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/307/ END:VEVENT BEGIN:VEVENT SUMMARY:On a crossover between two mechanisms of sound propagation in liqu ids DTSTART;VALUE=DATE-TIME:20240925T070000Z DTEND;VALUE=DATE-TIME:20240925T074000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-334@indico.bitp.kiev.ua DESCRIPTION:Speakers: Taras Bryk ()\nHydrodynamic theory forms the basis f or our understanding of the macroscopic propagation\nof sound in liquids\, while viscoelasticity points out solid-like elastic features at large fre quencies. However\, there is no understanding how the viscoelasticity mani fests in the mechanism of propagation of mesoscopic and short-wavelength a coustic excitations in liquids.\n We report solutions of the general ized Langevin equation for density-density time correlation functions of a liquid system in terms of dynamic eigenmodes within viscoelastic and ther mo-viscoelastic dynamic models. A comparison with molecular dynamics sompu ter simulations for supercritical Ar is performed. It is shown by analysis of extended dynamic eigenmodes in liquids how the crossover from hydrodyn amic mechanism of sound propagation to elastic one takes place. Our analys is of wavenumber-dependent eigenvector components of the sound modes makes evidence that the viscoelasticity of sound excitations is originated by g radual replacement of contribution from hydrodynamic density fluctuations by non-hydrodynamic stress fluctuations. A consequence of the sound viscoe lasticity for emergence of structural relaxation is shown.\n\nhttps://indi co.bitp.kiev.ua/event/13/contributions/334/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/334/ END:VEVENT BEGIN:VEVENT SUMMARY:Influence of the unit cell size of periodic electromagnetic metama terials on their optical properties DTSTART;VALUE=DATE-TIME:20240924T145500Z DTEND;VALUE=DATE-TIME:20240924T150000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-367@indico.bitp.kiev.ua DESCRIPTION:Speakers: Victor Gozhenko (Institute of Physics\, National Aca demy of Sciences of Ukraine)\nTo date\, the most of metamaterials used in diverse applications (from nanooptics and plasmonics to mobile communicati on and biophysics) are periodic structures consisting of spatially arrange d inclusions. In the theory of metamaterials\, they are treated as homogen eous media\, if their unit cell size $d$ (the lattice constant) is much sm aller than the wavelength $\\lambda$ of the incident electromagnetic wave the metamaterials operate with\, $d \\ll \\lambda$. A number of homogeniza tion theories have been proposed to calculate metamaterial's effective par ameters\, such as the effective permittivity $\\varepsilon_{\\textrm{eff}} $\, permeability $\\mu_{\\textrm{eff}}$\, and index of refraction $n_{\\te xtrm{eff}}$\, based on the geometry and material parameters of the metamat erial's inclusions. In practice\, however\, condition $d \\ll \\lambda$\, or\, equivalently\, $d / \\lambda \\ll 1$\, is not always met.\n\nIn the p resent work\, the properties of metamaterials are analyzed in a wider rang e of their relative unit cell size $d / \\lambda$ values for several types of the metamaterials' inclusions of practical interest. The optical refle ctance $R$ and transmittance $T$ of the metamaterials are numerically calc ulated based on the Lorentz volumetric averaging of the local electric and magnetic fields inside the unit cells\, rather than using recent metamate rials homogenization theories proposed in the last two decades.\n\nIt is s hown that behavior of the optical properties of metamaterials declines mor e and more from what is expected based on the homogenization concept\, as the relative unit cell size increases from small values $d / \\lambda \\ll 1$ (the quasistatic regime) to the unity (the intermediate operating regi me). In the latter regime\, a crucial role in the optical properties forma tion play the diffraction and interference effects in the metamaterials\, and the properties exhibit an oscillating behavior which cannot be predict ed within the homogenization concept.\n\nPublications:\n\nV. V. Gozhenko\, A. K. Amert\, and K. W. Whites\, Homogenization of periodic metamaterials by field averaging over unit cell boundaries: use and limitations\, New J . Phys. 15\, 043030 (2013) https://doi.org/10.1088/1367-2630/15/4/043030\n \nVictor V. Gozhenko\, Size Effects in Periodic Metamaterials\, arXiv:2301 .03518 [physics.optics] (2023) https://doi.org/10.48550/arXiv.2301.03518\n \nhttps://indico.bitp.kiev.ua/event/13/contributions/367/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/367/ END:VEVENT BEGIN:VEVENT SUMMARY:Low temperature behavior of the heat capacity of MWCNTs with Ø9. 4 nm: component of flexural dispersion for phonons DTSTART;VALUE=DATE-TIME:20240924T145500Z DTEND;VALUE=DATE-TIME:20240924T150000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-370@indico.bitp.kiev.ua DESCRIPTION:Speakers: Yuliia Horbatenko (B.Verkin Institute for Low Temper ature Physics and Engineering of the National Academy of Sciences of Ukra ine)\nM.S. Barabashko1\, M.I. Bagatskii1\, V.V. Sumarokov1\, A.I. Krivchik ov1\, \nA. Jeżowski2\, D. Szewczyk2\,3\, Y. Horbatenko1\n\n\n1B.Verkin In stitute for Low Temperature Physics and Engineering of NAS of Ukraine\,\n4 7 Nauky Ave.\, Kharkiv\, 61103\, Ukraine\n2 W. Trzebiatowski Institute for Low Temperatures and Structure Research\, Polish Academy of Sciences\, \n P.O. Box 1410\, 50-950 Wroclaw\, Poland\n3Low Temperature Laboratory\, Con densed Matter Physics Department\, Universidad Autónoma de Madrid\, Madri d\, Spain\n\ne-mail: msbarabashko@gmail.com\n\nLow-temperature specific he at C(T) of multi-walled carbon nanotubes (MWCNTs) was studied. Two sets o f modified\, milled and milled-oxidized MWCNTs with an average outer diame ter of 9.4 nm were used to measure specific heat in the temperature range of 1.8 to 275 K. The experimental results were compared with literature da ta for different carbon systems: bundles of single-walled carbon nanotubes (SWCNTs)\, graphite and other MWCNTs.\nThe initial MWCNTs were obtained b y the CVD method. The length of MWCNTs and parameters of defects (number a nd types) in MWCNTs were changed: 1) grinding of the initial nanotubes in a ball mill\; 2) the initial nanotubes were first oxidized and then milled . The figure shows low-temperature experimental heat capacity curves of gr ound (Sm)\, ground-oxidized (Sm-o) MWCNTs with outer diameters of Ø9.4 nm \, as well as\, for comparison\, original nanotubes (Si)\, bundles of SWNC Ts (Ø1.1 nm) and graphite. The analysis of the low-temperature behavior o f the heat capacity of carbon materials below 3 K was carried out under th e assumption that C(T) is determined primarily by phonons with sufficientl y long wavelengths (deformation waves). The specific heat C(T)\, described by the equation C(T) = A*T + B*T3+ D*T5. The coefficients A\, B and D wer e calculated and analyzed. The decrease in the length of nanotubes and the appearance of defects as a result of both grinding and oxidation with sub sequent grinding lead to an increase in heat capacity in the low-temperatu re region. The obtained negative D parameter indicated flexural dispersion for phonons. It was found that the magnitudes of the Debye (B) and flexur al dispersive components (D) depend on the structural parameters of nanot ubes: such as the diameter of individual nanotubes\, the average diameter of the bundle and the size of agglomerates. \n\n\nAcknowledgments: \nThis work has been supported by the National Research Foundation of Ukraine\n\n https://indico.bitp.kiev.ua/event/13/contributions/370/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/370/ END:VEVENT BEGIN:VEVENT SUMMARY:Features of the temperature dependences of the thermal conductivit y of composites and the Meyer-Neldel rule DTSTART;VALUE=DATE-TIME:20240924T145000Z DTEND;VALUE=DATE-TIME:20240924T145500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-376@indico.bitp.kiev.ua DESCRIPTION:Speakers: Yuliia Horbatenko (B.Verkin Institute for Low Temper ature Physics and Engineering of the National Academy of Sciences of Ukra ine)\nAn analysis of the temperature dependences of thermal conductivity κ(Т) of composite materials - graphene-multilayer graphene\, semiconduct or composites Bi0.5Sb1.5Te3 and In0.53Ga0.47As\, was carried out as well a s a comparison of their temperature dependences of κ(Т) with the thermal conductivity of similar materials\, which are formed by superlattices\, n anowires and hybrid nanostructures. The temperature dependence of the ther mal conductivity κ(Т) of these materials can be presented as the sum of two contributions – quasi-particle κp and coherence contributions κc: \n$κ = κp + κc$\, (1) \nwhich corresponds to two main mechanisms of hea t transfer [1]. In the case of orientationally ordered crystals\, thermal conductivity\, as a rule\, can be represented as: \n$κ = AT-1 + κ0$\, (2 ) \nwhere the first term is determined by the three-phonon scattering proc esses of quasiparticles (phonons)\, and the second term is related to the wave properties of phonons and their ability to tunnel between phonon band s corresponding to the acoustic and optical phonon branches in the real di spersion law [1]. \nIn the case where long-range order is present\, the va lue of the coherent contribution κc is usually small compared to the quas i-particle contribution κp\, but it becomes significant when no translati on order - then it takes place the glass-like behavior of thermal conducti vity – and it can be presented through an exponential dependence of the Arrhenius type: \n$κc = κ0∙exp(-E/T)$ (3) \nwith two characteristic p arameters: pre-exponential factor κ0 and energy E. It was shown that the temperature dependences of thermal conductivity with glassy behavior are q uite well described by expression (3). Also\, it is established that the p re-exponential factor κ0 depends linearly on the energy E. Such a relatio nship between these values was previously discovered in the electrical con ductivity of semiconductors (Meyer-Neldel rule) [2\, 3].\n\nReferences:\n[ 1] A.I. Krivchikov\, Y.V. Horbatenko\, O.A. Korolyuk\, O.O. Romantsova\, O .O. Kryvchikov\, D. Szewczyk & A. Jezowski. Exponential approximation of t he coherence contribution to the thermal conductivity of complex clathrate -type crystals. Materialia\, 32\, 101944 (2023).\n[2] A.I. Krivchikov & O. A. Korolyuk. Empirical universal approach to describing the thermal conduc tivity of amorphous polymers: Effects of pressure\, radiation and the Meye r–Neldel rule. Low Temperature Physics\, 50(4)\, 328-341 (2024). \n[3] W .V. Meyer and H. Neldel. Relation between the energy constant and the quan tity constant in the conductivity–temperature formula of oxide semicondu ctors\, Z. tech. Phys.\, 18(12): 588–593 (1937).\n\nhttps://indico.bitp. kiev.ua/event/13/contributions/376/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/376/ END:VEVENT BEGIN:VEVENT SUMMARY:Influence of the pH of aqueous sodium chloride solutions with diss olved carbon dioxide on the temperature interval of human vital activity DTSTART;VALUE=DATE-TIME:20240924T144500Z DTEND;VALUE=DATE-TIME:20240924T145000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-375@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksii Khorolskyi (Poltava V.G. Korolenko National Pedagogical University)\nTemporal changes in the temperature and concentra tion dependences of the pH value in aqueous sodium chloride solutions cont acting with atmospheric carbon dioxide have been studied experimentally. T he measurements are carried out in a temperature interval of (294–323) K for ion concentrations corresponding to (180–1600) water molecules per sodium or chlorine ion.\nThe pH value for dilute aqueous solutions of sodi um chloride is a sum of two components: reducible and irreducible. The red ucible component depends linearly on the temperature and\, therefore\, can not be responsible for the specific details of the human and mammalian lif e activities. Therefore\, the main parameters of the latter have to be cha racterized by the irreducible pH component\, which is an order of magnitud e smaller than the reducible component. The proportionality between the ir reducible pH component value and the sodium chloride concentration may tes tify that minor pH changes are associated with corresponding changes in th e salt composition of blood plasma that affect the state of human organism .\nThe pH relaxation time in aqueous NaCl solutions with dissolved atmosph eric carbon dioxide and its dependence on the temperature and the ion conc entration are calculated. The analysis of the obtained temperature depende nces of the pH relaxation time testifies that they are similar for various concentrations of NaCl ions in water. The principle of natural selection of the optimal states of aqueous salt solutions characterized by the tempe rature and the irreducible component of pH has been formulated for the fir st time: optimal are those states in which the pH relaxation time in aqueo us salt solutions is minimum.\nThe minimum points in the curves of the irr educible pH component for aqueous sodium chloride solutions are directly r elated to the temperatures that can be interpreted as the lower (approx. 3 0°C) and upper (approx. 42°C) limits of the temperature interval of the human and mammalian life activities. At the same time\, the minimum in a v icinity of the temperature of 37°C can be interpreted as the optimal temp erature for the vital activity of humans and mammals.\nSince the reducible and irreducible pH components behave themselves differently\, of particul ar importance becomes the issue concerning the conformational modification s of human serum albumin and other proteins\, which depend on the pH value . The addition of proteins will change the reducible pH component\, and th e conformational modification of albumin will be primarily induced by the electric fields of hydrogen cations\, which will directly affect the irred ucible pH component.\n\n[1] L.A. Bulavin\, N.P. Malomuzh\, O.V. Khorolskyi . Reducible and irreducible components of the pH value in dilute aqueous s olutions of sodium chloride. Ukrainian Journal of Physics\, 2023\, 68(3)\, 177–183. https://doi.org/10.15407/ujpe68.3.177\n\nhttps://indico.bitp.k iev.ua/event/13/contributions/375/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/375/ END:VEVENT BEGIN:VEVENT SUMMARY:Invisible states Potts model DTSTART;VALUE=DATE-TIME:20240924T144000Z DTEND;VALUE=DATE-TIME:20240924T144500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-325@indico.bitp.kiev.ua DESCRIPTION:Speakers: Mariana Krasnytska (Institute for Condensed Matter P hysics\, National Acad. Sci. of Ukraine\, Lviv\, 79011\, Ukraine)\nThe Pot ts model with invisible states was introduced to explain discrepancies bet ween theoretical predictions and experimental observations of phase transi tions in some systems where Zq symmetry is spontaneously broken [1]. It di ffers from the ordinary q-state Potts model in that each spin\, besides th e usual q visible states\, can be also in any of r so-called invisible sta tes. Spins in an invisible state do not interact with their neighbours but they do contribute to the entropy of the system. As a consequence\, an in crease in r may cause a phase transition to change from second to first or der. Potts models with invisible states describe a number of systems of in terest in physics and beyond and have been treated by various tools of sta tistical and mathematical physics. We aim to give a review of this fundame ntal topic based on our results [2-4]. Mainly\, our goal was to investigat e the energy-entropy interplay influence on the phase transition in the Po tts model with invisible states in 1D case [2] as well as on different gra ph topologies [3].\nWe acknowledge support from the National Research Foun dation of Ukraine\, Project 2023.03/0099 "Criticality of complex systems: fundamental aspects and applications".\n\n[1] S. Tanaka\, R. Tamura\, N. K awashima. J. Phys. Conf. Ser.\, 297 (2011) 012022.\n[2]. Petro Sarkanych\, Yurij Holovatch\, Ralph Kenna. Journ. Phys. A vol. 51 (2018) 505001\; Phy s. Lett. A vol. 381\, (2017) 3589-3593\n[3] M. Krasnytska\, P. Sarkanych\, B. Berche\, Yu. Holovatch\, R. Kenna. J. Phys. A: Math. Theor.\, 49(25) ( 2016) 255001\;\nP. Sarkanych\, M. Krasnytska. Cond. Matt. Phys.\, 26 (1) ( 2023) 13507.\n[4] M. Krasnytska\, P. Sarkanych\, B. Berche\, Yu. Holovatch \, R. Kenna. Eur. Phys. J. Spec. Top. 232\, 1681–1691 (2023).\n\nhttps:/ /indico.bitp.kiev.ua/event/13/contributions/325/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/325/ END:VEVENT BEGIN:VEVENT SUMMARY:Evaluating Benchmarks for the Effectiveness of Infrared Camouflage Coatings DTSTART;VALUE=DATE-TIME:20240924T143500Z DTEND;VALUE=DATE-TIME:20240924T144000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-317@indico.bitp.kiev.ua DESCRIPTION:Speakers: Ye.O. Melezhyk (V. Lashkaryov Institute of Semicondu ctor Physics\, NASU)\nContemporary research in defense technology focuses extensively on concealing various objects from infrared (IR) reconnaissanc e. Numerous camouflage coatings are available in the market\, designed to mask IR radiation emitted by targets. Manufacturers often claim that these coatings significantly reduce the mean apparent temperature difference ( ΔT) between the object and its background. However\, a critical scientifi c question remains: how does the reduction in ΔT correlate with the actua l decrease in maximum detection range (MDR) achieved by thermal imaging sy stems?\n\nA wide range of cooled and uncooled portable thermal imagers exi sts for the 3-5 μm and 8-12 μm spectral ranges. Their detection capabili ties are constrained by both spatial resolution and thermal sensitivity\, characterized by the noise equivalent temperature difference (NETD). To es timate the MDR reduction due to target temperature contrast masking\, it i s valuable to evaluate the MDR for several commercially available thermal imagers at distances where their sensitivity for chosen object size is not restricted by spatial resolution. According to NATO Standard STANAG 4347\ , the MDR for a target can be determined by graphically solving an equatio n. The left-hand side of this equation represents the simple exponential d ecay of ΔT with distance\, while the right-hand side denotes the minimum resolvable temperature difference (MRTD) of the thermal imager\, which is also dependent on distance and target dimensions. The MRTD for a high-reso lution thermal imager in the 3-5 μm range was obtained from literature [1 ].\n\nOur modeling aimed to assess how a 50% reduction in target ΔT affec ts the MDR and to evaluate the significance of this change relative to pot ential variations due to adverse weather conditions. We modeled targets wi th ΔT = 4 K (uncamouflaged) and ΔT = 2 K (camouflaged)\, using atmospher ic absorption coefficients of k = 0.2 1/km (good transmission conditions) and k = 1 1/km (limited transmission conditions). The dimensions of the te st target were set at 1x1 m2.\n\nThe modeling results for the 3-5 μm rang e are presented in the Figure 1. The MDR is determined at the intersection point of the ΔT and MRTD curves. Our findings indicate that a 50% decrea se in ΔT has only a slight impact on MDR reduction under any weather cond itions. Consequently\, effective IR camouflage coatings should provide a s ubstantially greater reduction in the observed temperature difference betw een the target and background. Furthermore\, our modeling revealed that th e MDR for a target with a fixed ΔT can vary by several times depending on weather conditions. Similar modeling was also conducted for the 8-12 μm range.\n\nThis study was supported by NRFU project #2023.04/0026.\n\n1. Ba rela\, J.\, Firmanty\, K.\, & Kastek\, M. (2021). Measurement and analysis of the parameters of modern long-range thermal imaging cameras. Sensors\, 21(17)\, 5700. https://doi.org/10.3390/s21175700.\n\n\nFig.1. The modelin g results for the 3-5 μm range MDR for variable weather conditions\, for camouflaged and uncamouflaged target.\n\nhttps://indico.bitp.kiev.ua/event /13/contributions/317/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/317/ END:VEVENT BEGIN:VEVENT SUMMARY:Supercritical propagation of nonlinear magnetization wave through an antiferromagnetic magnonic crystal DTSTART;VALUE=DATE-TIME:20240924T143000Z DTEND;VALUE=DATE-TIME:20240924T143500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-306@indico.bitp.kiev.ua DESCRIPTION:Speakers: Ihor Syzon (National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute»)\nAnalytical model of a nonl inear magnetization wave (MW) propagating through one-dimensional antifer- romagnetic magnonic crystal comprised of two sorts of antiferromagnets (AF M) is proposed for supercritical mode when the MW velocity exceeds the cri tical velocity of MW in both antiferromagnets AFMs or at least in one of t hem. Both AFMs that comprise the magnonic crystal are assumed to be two-su blattice uniaxial ones. The Landau-Lifshitz equations have been used in th e sigma model with account for the exchange bias between magnetic sublat-t ices of both AFMs\, the magnetic anisotropy\, the magnetic dipole-dipole i nteraction and the Dzyaloshynskii-Moriya interaction. The boundary conditi ons for the Néel vector (with the exchange bias between magnetic sublatti ces of both AFMs taken into account) are applied on the interface between two AFMs. The discrete sets of frequencies and velocities for the consider ed MW are obtained. Analysis of the results shows that the nonlinear MW is reflection-less\, phase-coherent and possesses a number of parameters tha t can be considered as degrees of freedom for encod-ing information. These findings open up new possibilities of digital data processing utilizing n onlinear MW propa-gating through antiferromagnetic magnonic crystal in sup ercritical mode.\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/306 / LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/306/ END:VEVENT BEGIN:VEVENT SUMMARY:The electric field quantum control of spin-waves dynamics in easy- axis antiferromagnets DTSTART;VALUE=DATE-TIME:20240924T142500Z DTEND;VALUE=DATE-TIME:20240924T143000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-352@indico.bitp.kiev.ua DESCRIPTION:Speakers: Olha Boliasova (State Research Institution «Kyiv Ac ademic University»)\nO. O. Boliasova$^{1\,2}$ and V. N. Krivoruchko$^3$\n $^1$State Research Institution «Kyiv Academic University»\n36 Academicia n Vernadsky Boulevard\, 03142\, Kyiv\, Ukraine\,\n$^2$G. V. Kurdyumov Inst itute for Metal Physics of the N.A.S. of Ukraine\n36 Academician Vernadsky Boulevard\, 03142\, Kyiv\, Ukraine\, and\n$^3$Donetsk Institute for Physi cs and Engineering named after O.O. Galkin of the NAS of Ukraine\,\n46 Nau ki Avenue\, 03028\, Kyiv\, Ukraine\n\nMagnetic materials are widely used i n current computers and have the potential to expand their applicability [ 1]. The most important step forpractical applications is understanding how to manipulate spin dynamics in magnetic materials efficiently. One method that has been actively discussed is usingan electric field. It is well kn own that spin waves with different chirality exist in antiferromagnets\, h owever\, in the absence of external influence these spin waves are degener ated. An electric\, E\, field can split them and manipulate each polarizat ion differently. This phenomenon is an example of a topological effect kno wn asthe Aharonov-Casher effect [2\,3]. In the linear order approximation\ , this effect can be accounted for by adding a term to the system’s free energy expression like the Dzyaloshinskii-Moriya interaction.\nWe present the results on the E-field effect on chirality-dependent spin-waves dynam ics in a two-sublattice easy-axis antiferromagnet [4\,5]. The research was conducted using a phenomenological approach based on the Landau-Lifshitz- Gilbert equations. It was shown that the electric field can split spin wav es of different chirality\, and the magnitude of the splitting is proporti onal to the magnitude of the electric field. This splitting can be further enhanced by applying a magnetic field. More details are provided on the E -field effect on the propagation of spin waves and their damping length. T he electric field affects the propagation of the right-handed and left-han ded spin waves differently\, while a small magnetic field doesn`t influenc e the damping length. These findings could be useful for field-effect tran sistors or interferrometric devices [6] based on spin waves. Since the app lication of the electric field is easier than that of a large magnetic fie ld\, the Aharonov-Casher effect has great potential for practical applicat ions.\nThe authors acknowledge the financial support by the STCU\, project “Magnetism in Ukraine Initiative”\, project Agreement No. 9918.\n\nht tps://indico.bitp.kiev.ua/event/13/contributions/352/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/352/ END:VEVENT BEGIN:VEVENT SUMMARY:DNA condensation induced by Li$^+$ counterions DTSTART;VALUE=DATE-TIME:20240924T142000Z DTEND;VALUE=DATE-TIME:20240924T142500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-338@indico.bitp.kiev.ua DESCRIPTION:Speakers: Dmytro Piatnytskyi (Bogolyubov Institute for Theoret ical Physics)\nDNA is a highly charged molecule that is neutralized by pos itively charged metal or molecular ions (counterions). The neutralization of DNA by these counterions induces various effects\, including the format ion of DNA-DNA contacts that lead to further condensation of the macromole cule. The effect of DNA condensation has been widely observed for highly c harged counterions (≥3+). For divalent counterions\, DNA condensation is sometimes observed\, whereas with monovalent ions\, it is generally consi dered impossible due to insufficient neutralization of the double helix's charge required to form stable DNA-DNA contacts. However\, the idea that D NA cannot condense with monovalent ions overlooks the interplay between wa ter molecules in the DNA hydration shell and those in the hydration shell of counterions\, which can play an essential role in the interaction of DN A duplexes. Li$^+$ is highly hydrated and it is localized within a stable tetrahedron formed by four oxygen atoms of water molecules. Considering th e structural complementarity of the DNA phosphate groups to the hydration shell of Li$^+$ ions [1]\, the formation of Li-mediated DNA-DNA contacts m ay occur. To elucidate the possibility of forming stable Li$^+$ crosslinks between different DNA double helices\, the molecular mechanisms of their formation are studied in the present work. Atomistic molecular dynamics si mulations of five DNA fragments in a simulation box with LiCl concentratio n 0.1 M and 1.0 M of salt were carried out. As a result of our study\, the possible configurations of crosslinks between phosphate groups of differe nt DNA fragments were determined. To validate the obtained results\, the v ibrational spectra of characteristic complexes were calculated using quant um-chemical methods and compared with existing experimental data. This wor k demonstrates that DNA-DNA contacts mediated by Li$^+$ can form in aqueou s solutions with a high concentration of DNA and LiCl salt\, supporting th e idea of DNA condensation by Li$^+$ counterions. \n\n[1] Lyubartsev\, A. P.\; Laaksonen\, A. Molecular Dynamics Simulations of DNA in Solution with Different Counter-Ions. J. Biomol. Struct. Dyn. 1998\, 16 (3)\, 579–592 . https://doi.org/10.1080/07391102.1998.10508271.\n\nhttps://indico.bitp.k iev.ua/event/13/contributions/338/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/338/ END:VEVENT BEGIN:VEVENT SUMMARY:Model of effective permittivity for dense ferroelectric nanocompos ites DTSTART;VALUE=DATE-TIME:20240924T141500Z DTEND;VALUE=DATE-TIME:20240924T142000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-353@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksii Bereznykov ()\nExisting theoretical models o f ferroelectric nanocomposites use the effective medium approximation to d escribe their dielectric and conductive properties. The most common effect ive medium models (Landau linear mixture approximation\, Maxwell-Garnett m odel\, Bruggeman model\, etc.) may be invalid for dense nanocomposites whe n the volume fraction of ferroelectric inclusions exceeds 20-30%. We have proposed several modifications\, such as averaging over particle size\, fi nite conductance of the screening shell\, and the dipole-dipole cross-inte raction effects between the electric polarization (i.e.\, their electric d ipoles) of different ferroelectric nanoparticles separated by shells and a matrix.\nThe Lichtenecker-Rotter model\, which is free from the volume fr action limitations\, was used to estimate the effective dielectric constan t $\\epsilon_{eff}$ of the nanocomposite without taking into account the e ffects of cross-interaction. However\, the presence of small particles (si ze 30 nm or less) should be taken into account\, as dipole-dipole cross-in teractions can lead to the formation of polar clusters\, where the ferroel ectric dipoles of single-domain nanoparticles are strongly correlated\, an d the correlations determine the effective dielectric response of the comp osite.\nThe presence for larger submicron particles (size 300 nm or more)\ , which usually split into ferroelectric domains\, the cross-interaction e ffects can lead to correlated motion of ferroelectric domain walls in neig hboring nanoparticles\, which\, in turn\, make a significant contribution to the temperature and frequency behavior of the dielectric response of th e composite.\nThe dependence on $\\epsilon_P(T\, \\theta\, \\omega)$ of th e frequency $\\omega$ and the temperature of the local transition $\\theta $ of nanoparticles and their polar clusters in a ferroelectric polymer nan ocomposite was analyzed taking into account the dipole-dipole cross-intera ctions. As a result\, the equation for $\\theta$. was obtained. This equat ion was successfully applied to calculate the dielectric constant of dense PVDF nanocomposites with 20-30 vol.% of barium titanate nanoparticles. Th e obtained results can be used for the prediction and development of the f lexible and cheap nanocomposite with superior polar and dielectric propert ies for usage in non-volatile memory cells\, energy-saving elements\, modu lators and sensors.\n\nThe work of P.O.S. and M.A.N. is funded by the Nati onal Research Foundation of Ukraine (project “Manyfold-degenerated metas table states of spontaneous polarization in nanoferroics: theory\, experim ent and perspectives for digital nanoelectronics”\, grant N 2023.03/0132 )\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/353/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/353/ END:VEVENT BEGIN:VEVENT SUMMARY:Polaronic model of the Giant Dielectric and Pyroelectric Responses of Ferroelectric Fine-Grained Ceramics DTSTART;VALUE=DATE-TIME:20240924T141000Z DTEND;VALUE=DATE-TIME:20240924T141500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-368@indico.bitp.kiev.ua DESCRIPTION:Speakers: Eugene Eliseev (Frantsevich Institute for Problems i n Materials Science\, National Academy of Sciences of Ukraine)\nWe describ ed the anomalous temperature behavior of the giant dielectric response and losses using the core-shell model for ceramic grains and modified Maxwell -Wagner approach. We assume that core shells and grain boundaries\, which contain high concentration of space charge carriers due to the presence of graphite inclusions in the inter-grain space\, can effectively screen wea kly conductive ferroelectric grain cores. \nWe considered several possible mechanisms\, which can lead to the giant values of the relative dielectri c permittivity accompanied by the very high values of dielectric losses in the strongly inhomogeneous ferroelectric-semiconducting ceramics. \nThe f irst mechanism is the effect of “geometric” capacitance\, which could appear in the highly porous mixtures of the insulating and conducting incl usions. In this case the effective surface area of the capacitor could be much larger than the electrodes area\, and the effective area could accumu late the space charge. Note that the geometric capacitance effect contribu tion could be verified by measuring the capacitance of the ceramic samples of different cutting angles\, thickness\, electrode area\, frequency\, an d temperature.\nThe second mechanism is the Maxwell-Wagner effect [1]\, wh ich could lead to the apparent enhancement of the dielectric response in t he dielectric-semiconducting mixture in the presence of insulating polar g rains\, screening shells and conducive graphite inclusions. In principle a ll conductivity effects in the inhomogeneous media are strongly inter-wine d and closely related with possible electric percolation effects. The poss ible roles and relative contributions of the different conductivity effect s were considered with the help of the different theoretical models.\nAcco rding to the effective media model proposed by Liu et al. [2]\, the one ca n consider two (or more) layers representing all grain cores\, their scree ning shells and grain boundaries\, graphite inclusions and inter-grain spa ce in the Maxwell-Wagner approach. One of the “effective” layers corre sponds to weakly-conductive grain cores\, and the other corresponds to all stronger conductive regions (such as screening shells\, grain boundaries and/or inter-grain space). The layers are characterized by the effective d ielectric permittivity and conductivity for grain cores\, grain boundaries and/or inter-grains. These effective parameters are temperature and/or fr equency dependent.\nThe superparaelectric-like state with a giant dielectr ic response can appear in the paraelectric shells and inter-grain space du e to the step-like thermal activation of localized polarons in the spatial regions\, being in agreement with experimentally observed frequency-depen dent transition of the electro-transport mechanism [3]. Obtained results c an be the key for the description of complex electrophysical properties in herent to the strongly inhomogeneous media with electrically coupled insul ating ferroelectric nanoregions and semiconducting superparaelectric-like regions.\nThe work of A.N.M. and E.A.E. are funded by the National Researc h Foundation of Ukraine (projects “Manyfold-degenerated metastable state s of spontaneous polarization in nanoferroics: theory\, experiment and per spectives for digital nanoelectronics”\, grant N 2023.03/0132 and “Sil icon-compatible ferroelectric nanocomposites for electronics and sensors ”\, grant N 2023.03/0127)\n[1] K.W. Wagner\, Arch Elektrotech 2\, 371 (1 914)\; https://doi.org/10.1007/BF01657322\n[2] L. Liu\, S. Ren\, J. Liu\, F. Han\, J. Zhang\, B. Peng\, D. Wang\, A. A. Bokov\, and Z.-G. Ye\, Phys. Rev. B 99\, 094110 (2019)\, https://doi.org/10.1103/PhysRevB.99.094110\n[ 3]. O. S. Pylypchuk\, S.E. Ivanchenko\, M.Y. Yelisieiev\, A. S. Nikolenko\ , V.I. Styopkin\, B. Pokhylko\, V. Kushnir\, D.O. Stetsenko\, O. Bereznyko v\, O.V. Leschenko\, E.A. Eliseev\, V.N. Poroshin\, N.V. Morozovsky\, V.V. Vainberg\, and A.N. Morozovska. https://doi.org/10.48550/arXiv.2407.01108 (http://arxiv.org/abs/2407.01108)\n\nhttps://indico.bitp.kiev.ua/event/13 /contributions/368/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/368/ END:VEVENT BEGIN:VEVENT SUMMARY:Microscopic derivation of the generalixed Bohr Hamiltonian DTSTART;VALUE=DATE-TIME:20240924T140500Z DTEND;VALUE=DATE-TIME:20240924T141000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-374@indico.bitp.kiev.ua DESCRIPTION:Speakers: Alexey Dzyublik (Institute for Nuclear Research of N ASU)\nThe Bohr’s Hamiltonian is one of the main cornerstones of the nucl ear structure theory. It was derived by Bohr [1]\, treating the nucleus a s a liquid spherical drop with uniform density and sharp surface\, perform ing quadrupole vibrations with small amplitude. During such oscillations a t any moment of time the nucleus attains an ellipsoidal shape\, retaining its volume constant due to small compressibility of the nuclear matter.\n Following the microscopic theory [2]\, where the kinetic energy operator of the nucleus has been expressed in terms of the independent set of 3N co llective variables\, we constructed the collective Hamiltonian for nuclei with arbitrary deformation [3]\, which recovers the results of Bohr [1] at β \n\nhttps://indico.bitp.kiev.ua/event/13/contributions/374/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/374/ END:VEVENT BEGIN:VEVENT SUMMARY:Constraints on the parameters of HNL and baryon asymmetry of the U niverse DTSTART;VALUE=DATE-TIME:20240924T140000Z DTEND;VALUE=DATE-TIME:20240924T140500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-351@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksandr Khasai (Bogolyubov Institute for Theoretic al Physics of the National Academy of Sciences of Ukraine)\nOne of the sim plest renormalizable extensions of the SM is the minimal neutrino extensio n of the Standard Model $\\nu$MSM\, proposed in 2005 [1\, 2]. This modific ation introduces three righthanded neutrinos or heavy neutral leptons (HNL ). The lightest sterile neutrino is identified as a dark matter particle. The other two sterile neutrinos are much heavier\, with nearly identical m asses\, and are responsible for generating the baryon asymmetry observed i n the Universe. The observable parameters of the $\\nu$MSM Lagrangian are given in [3]\n$$\\begin{align}\n & S_{\\alpha\\beta} \\equiv (F M^{-1\\ ast}M^{-1} F^\\dagger)_{\\alpha\\beta} = \\sum_I S^I_{\\alpha\\beta} = \\s um_I F_{\\alpha I}F^\\dagger_{I \\beta} M_I^{-2}\,\\\\\n & R_{\\alpha\\ beta} = \\sum_I R^I_{\\alpha\\beta} = \\sum_I S^I_{\\alpha\\beta}\\ln\\fra c{M_I}{M_W} = \\sum_I F_{\\alpha I}F^\\dagger_{I \\beta} M_I^{-2} \\ln\\fr ac{M_I}{M_W}.\n\\end{align}$$\nIn the $\\nu$MSM framework\, the lightest s terile neutrino\, which serves as a long-lived dark matter particle\, is u ndetectable in collider experiments. Therefore\, we focus on a simplified scenario that extends the SM by incorporating only two heavy sterile neutr inos. A straightforward relationship has been derived between the experime ntally observed quantities (the elements of the matrices Sαβ and Rαβ). This relationship holds for cases where active neutrinos have non-zero ma sses and where the masses of the heavy sterile neutrinos vary.\n$$\\begin{ equation}\n S_{\\alpha \\beta}\\Bigl(M_1\\ln \\frac{M_2}{M_W}+M_2\\ln \ \frac{M_1}{M_W}\\Bigr)=R_{\\alpha \\beta}(M_1+M_2)\,\\quad S_{\\alpha \\al pha} S_{\\beta \\beta} = |S_{\\alpha \\beta}|^2 \\quad\n R_{\\alpha \\a lpha} R_{\\beta \\beta} = |R_{\\alpha \\beta}|^2.\n\\end{equation}$$\nBuil ding on the results of [1]\, we have translated the constraints on baryon asymmetry generation in the early Universe into observable parameters $S_{ \\alpha \\beta}$ and $R_{\\alpha \\beta}$. We concluded that the actual va lues of elements of $\\hat R$ and $\\hat S$ matrices are many orders of ma gnitude less than existing experimental constraints. Results of our invest igation are presented in detail in [4].\nAcknowledgment. The work of V.G. and O.Kh. was supported by the National Research\nFoundation of Ukraine un der project No.2023.03/0149.\n\n[1] T. Asaka and M. Shaposhnikov\, Phys. L ett. B\, 620\, 17 (2005).\n[2] S. Blanchet\, T. Asaka and M. Shaposhnikov\ , 151 (2005).\n[3] R. Coy and M. Frigerio\, Phys. Rev. D 99\, 095040 (2019 ).\n[4] V. Gorkavenko\, O. Khasai\, O. Ruchayskiy\, M. Tsarenkova\, arXiv: 2408.02107 [hep-ph].\n\nhttps://indico.bitp.kiev.ua/event/13/contributions /351/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/351/ END:VEVENT BEGIN:VEVENT SUMMARY:Spontaneous magnetization and effective interactions in QGP at hig h temperature DTSTART;VALUE=DATE-TIME:20240924T135500Z DTEND;VALUE=DATE-TIME:20240924T140000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-372@indico.bitp.kiev.ua DESCRIPTION:Speakers: Volodymyr Skalozub (Oles Honchar Dnipro National Uni versity)\nIn quark-gluon plasma (QGP)\, at higher deconfinement temperat ures $T \\ge T_d$ the spontaneous generation of color magnetic fields\, $ b^3(T)\, b^8(T) \\not = 0$ (3\, 8 are color indexes)\, and usual magnetic field $b(T) \\not = 0$ happens. Simultaneously\, the Polyakov loop a nd/or algebraically related to it $A_0(T)$ condensate\, which is solutio n to Yang-Mills imaginary time equations\, are also created.\nUsually\, in analytic quantum field theory these effects are investigated independ ently of each other within the effective potentials having different mathe matical structures.\nThe common generation of these condensates was detec ted in lattice Monte Carlo simulations.\n\nRecently\, with the new typ e two-loop effective potential\, which generalizes the known integral rep resentation for the Bernoulli polynomials and takes into consideration the magnetic background\, this effect has been derived analytically.\n The corresponding effective potential $W(T\, b^3\, A_0 )$ was inv estigated either in SU(2) gluodynamics or full QCD. The gauge fixing inde pendence of it was proved within the Nielsen identity approach. The valu es of magnetic field strengths at different temperatures were calculated and the mechanism of stabilizing fields due to $A_0(T)$ condensate has been discovered. In the present review\, we describe this important phen omenon in more details\, as well as a number of specific effects happeni ng due to vacuum polarization at this background. They could serve as t he signals of the QGP creation in the heavy ion collision experiments.\ n \nKey words: spontaneous magnetization\, high temperature\, asymptotic f reedom\, effective potential\, $A_0$ condensate\, effective charge\, effec tive vertexes.\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/372/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/372/ END:VEVENT BEGIN:VEVENT SUMMARY:The development of Bogolyubov reduced description method in the ap plication to spin and quasispin systems DTSTART;VALUE=DATE-TIME:20240924T134500Z DTEND;VALUE=DATE-TIME:20240924T135000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-357@indico.bitp.kiev.ua DESCRIPTION:Speakers: Serhiy Lyagushyn (Oles Honchar Dnipro National Unive rsity)\n**The development of Bogolyubov reduced description method\nin the application to spin and quasispin systems**\nSokolovsky A. I.\, Lyagushyn S. F.\n*Oles Honchar Dnipro National University*\nThe reduced description method (RDM) is based on the Bogolyubov’s idea that at large time the n on-equilibrium state evolution of a macroscopic system can be described wi th the limited number of parameters. The way to the right choice of such p arameters and constructing the equations of time evolution for them was op ened by the works of Kharkiv school in statistical physics [1]. Since earl y 2000-ies the authors deal with applying the proposed technique to Dicke superradiance – the unique phenomenon of emitter system self-organizatio n in the process of reaching the equilibrium state from excited one. We ar e interested in a more detailed picture of correlation development both in emitter and field subsystems. The problem of correlator decoupling which arises in the Bogolyubov method of boson variable elimination [2]\, seems worthy of attention. In RDM\, including the binary correlation functions i nto the set of reduced description parameters (RDPs) results in the necess ity of calculating the averages with quasi-equilibrium Hamiltonians where such new parameters are present. Usually\, two-level electromagnetic emitt ers are described using the quasispin operators constructed with Pauli mat rices. While considering the acoustic superradiance\, spin and phonon oper ators are necessary for the Hamiltonian construction. The operator forms p rove to be the same for boson fields of different nature. Thus\, we face t he problem of averaging in the case when the exponential statistical opera tor includes a quadratic form of spin operators in the exponent that canno t be done exactly. \nIn our recent papers [3\, 4]\, a new approach consist ing of introducing additional small parameter in the theory of relaxatio n processes in spin systems has been proposed. While the spin-boson intera ction constant is a customary small parameter in the specified theory\, we put forward the idea of accounting for small deviations of correlation fu nctions taken as RDPs from their values calculated in the picture with the only RDP describing the state of a spin (quasispin) system – the excita tion degree of the emitter subsystem ${{\\eta }_{1}}$ (${{s}^{z}}=\\sum\\l imits_{1\\le i\\le N}{s_{i}^{z}}$ in usual designations). Restricting ours elves with the concentrated Dicke model\, we can use the known equation fo r ${{s}^{z}}$ possessing the integral of motion including the binary corre lation function $\\left\\langle {{{\\hat{s}}}^{+}}{{{\\hat{s}}}^{-}} \\rig ht\\rangle $. In the theory of superradiance using $\\left\\langle {{{\\ha t{s}}}^{+}}{{{\\hat{s}}}^{-}} \\right\\rangle $ as an independent RDP ${{\ \eta }_{2}}$ (${{\\hat{\\eta }}_{2}}={{\\hat{s}}^{+}}{{\\hat{s}}^{-}}$)\, we construct the quasi-equilibrium statistical operator of RDM ${{\\rho }_ {q}}={{e}^{\\Omega -{{Z}_{1}}{{{\\hat{\\eta }}}_{1}}-{{Z}_{2}}{{{\\hat{\\e ta }}}_{2}}}}$ implying the condition of smallness of the deviation $\\del ta {{\\eta }_{2}}=Sp({{\\rho }_{q}}-\\rho _{q}^{0}){{\\hat{\\eta }}_{2}}$\ , i.e. difference between correlation function obtained with such operator and those of RDM model with ${{\\eta }_{1}}$ only $\\rho _{q}^{0}={{e}^{{ {\\Omega }^{0}}-Z_{1}^{0}{{{\\hat{\\eta }}}_{1}}}}$. We use $\\delta {{\\e ta }_{2}}$ as a new small parameter of the order $\\mu $ and the statistic al operator ${{\\rho }_{q}}$ can be expressed via $\\rho _{q}^{0}$ in the form of μ power expansion. Thus\, we obtain expressions for spin average deviations with an error up to $\\mu^{3}$ and evolution equations for ${{\ \eta }_{1}}$\, ${{\\eta }_{2}}$\, and boson RDPs ${{n}_{k}}$. The solved p roblem relates to cumbersome calculations but only averages with linear fo rms of spin operators and quadratic forms of boson operators are needed. T he technique of averaging for spin operators was improved in the framework of our activities. The results are applicable for different versions of D icke model and Wagner model of acoustic superradiance.\n1. Akhiezer\, A. I . Methods of Statistical Physics / A. I. Akhiezer\, S. V. Peletminskii. – Oxford: Pergamon Press\, 1981. – 450 p.\n2. Bogolyubov\, N. N. (Jr.) Sverkhizlucheniye / N. N. Bogolyubov (Jr.)\, A. S. Shumovsky. – Dubna: JINR\, 1987\, JINR publication P17-87-176. – 88 p.\n3. Lyagushyn\, S. F. Taking into account the influence of correlations on the system dynamics in the reduced description method / S. F. Lyagushyn\, A. I. Sokolovsky // Journal of Physics and Electronics. –2023 – Vol. 31(1). – P. 7 – 1 7. https://doi.org/10.15421/332302\n4. Sokolovsky\, A. I. Dynamics of a sy stem of two-level emitters in the Dicke model taking into account small co rrelations between them / A. I. Sokolovsky\, S. F. Lyagushyn // Journal of Physics and Electronics. –2023 – Vol. 31(2). – P. 88 – 110. https ://doi.org/10.15421/332326\n\nhttps://indico.bitp.kiev.ua/event/13/contrib utions/357/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/357/ END:VEVENT BEGIN:VEVENT SUMMARY:Nonequilibrium protection effect and spatial localization of noise -induced fluctuations: gas flow scattering on partially penetrable obstacl e DTSTART;VALUE=DATE-TIME:20240924T134000Z DTEND;VALUE=DATE-TIME:20240924T134500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-366@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksandr Kliushnichenko (Institute of Physics\, Nat ional Academy of Sciences of Ukraine)\nThe scattering of gas flow on an ob stacle can lead to the formation of nonequilibrium steady states (NESS)\, such as stationary obstacle wakes. These systems may undergo nonequilibriu m phase transitions\, resulting in the emergence of nonlinear steady-state gas structures under critical conditions. One notable example is the form ation of a stratum-like\, or two-domain\, gas structure ahead of the obsta cle due to the blockade effect in the gas [1-5]. This structure can be int erpreted as the growth of a dense gas phase nucleus near the obstacle\, wh ich acts as a nucleation center.\n\nIn our study\, we focus on a quasi-one -dimensional driven lattice gas doped with static impurities within a narr ow channel with ring topology [1]. The obstacle is modeled as a transverse channel cell partially occupied by impurity particles\, and the system is driven by a nonconservative field. We utilize a combination of the local equilibrium approach and mean-field approximation to describe the NESSs an d gas fluctuations near them.\n\nOur findings reveal that this nonequilibr ium transition is associated with the emergence of a local invariant. Spec ifically\, the state of the obstacle behaves as a local first integral (or adiabatic invariant)\, becoming insensitive to fluctuations in the gas an d the external driving noise.\n\nBelow the transition\, the gas flow is sc attered by the impurity\, the structural defect of the lattice. Above the transition\, the gas flow is scattered by the gas domain wall\, the defect of the gas density distribution. This leads to the protection effect of t he obstacle state against gas fluctuations\, manifesting as a strong local ization of fluctuations near the topological defect (domain wall) and thei r complete suppression at the obstacle. Additionally\, gas fluctuations de monstrate strong anti-correlated behavior at the left and right sides of t he impurity. These effects are similar to the skin effect and edge-edge co rrelation effect in non-Hermitian systems [6].\n\nReferences:\n\n[1] S.P. Lukyanets\, O.V. Kliushnichenko\, Phys. Rev. E **109**\, 054103 (2024). ht tps://doi.org/10.1103/PhysRevE.109.054103\n[2] S. A. Janowski and J. L. Le bowitz\, Phys. Rev. A **45**\, 618 (1992).\n[3] K. Mallick\, Physica A **4 18**\, 17 (2015). https://doi.org/10.1016/j.physa.2014.07.046\n[4] A. Chum ak and A. Tarasenko\, Surf. Sci. **91**\, 694 (1980)\; A. A. Tarasenko\, P . M. Tomchuk\, and A. A. Chumak\, Fluctuations in the Bulk and on the Surf ace of Solids (Naukova Dumka\, Kyiv\, 1992).\n[5] D. N. Zubarev\, Nonequil ibrium Statistical Thermodynamics (Plenum Press\, New York\, 1974).\n[6] S . Shankar\, A. Souslov\, M.J. Bowick\, M.C. Marchetti\, and V. Vitelli\, N at. Rev. Phys. **4**\, 380 (2022). https://doi.org/10.1038/s42254-022-0044 5-3\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/366/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/366/ END:VEVENT BEGIN:VEVENT SUMMARY:Spin-boson description of the temporal behavior of the dynamical s ystem with time-dependent coupling to the environment DTSTART;VALUE=DATE-TIME:20240924T133500Z DTEND;VALUE=DATE-TIME:20240924T134000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-355@indico.bitp.kiev.ua DESCRIPTION:Speakers: Yevgen Shevchenko (Bogolyubov Institute for Theoreti cal Physics\, National Academy of Sciences of Ukraine)\nThis work shows ho w a kinetic process is formed in a dynamic system that is in a non-station ary coupling with the environment. It is assumed that the environment has a large number of degrees of freedom and therefore transitions in a dynami c system do not change the state of the environment. However\, due to the openness of a dynamic system\, the environment is capable of modifying bot h the states of the system and its energy levels. We are considering a qua ntum dynamic system\, where the exchange of energy between the system and the environment is carried out through vibrational quanta (phonons). Using the method of nonequilibrium statistical mechanics\, kinetic equations ar e obtained that describe the time evolution of the density matrix of a dyn amic system under conditions of strong (polaron) coupling with vibrational modes of both the environment and the system. The difference from a simil ar type of research is that the coupling between the electronic states of the system and its vibration states is assumed to be time-dependent. We pr oposed a unitary-transformation\, which made it possible to take into acco unt this non-stationary coupling directly in the operator responsible for transitions between states of the system. This opened up the possibility o f using the perturbation method to derive the master equation for the prob abilities of occupying system states. As an example of the application of non-stationary polaron transformation\, the kinetics of establishing the p robabilities of occupation of electronic states of an open TLS is consider ed.\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/355/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/355/ END:VEVENT BEGIN:VEVENT SUMMARY:Subensembles of magnetized particles in random electric fields DTSTART;VALUE=DATE-TIME:20240924T133000Z DTEND;VALUE=DATE-TIME:20240924T133500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-339@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksandr Cherniak (Bogolyubov Institute for Theoret ical Physics)\nTransport processes of a passive scalar in random velocity fields are observed in plasma systems\, atmosphere\, oceanic currents\, et c. The task of the theoretical description is to reproduce the temporal ev olution of an ensemble of particles moving in such a field based on the kn own statistical characteristics of the velocity or force fields. The most known example is Brownian motion\, the feature of which is the presence of two time scales. That is\, the time of collisions\, or the time of correl ations of random fields\, is much shorter than the time of system\, or the particle distribution function\, evolution. Then\, as is known\, the mean squared displacement of the particles\, or the second moment of the distr ibution function\, is proportional to the system evolution time. The distr ibution of particles\, which at the initial moment of time were concentrat ed at the origin of the coordinates\, preserves the Gaussian shape\, which evolves according to the mean squared displacement\, and the particle dif fusion coefficient in such fields is a constant value. \nMore complicated and more interesting is the transport of particles in random fields\, the correlation time of which is not small compared to the time of evolution o f the system. An example of such a system is charged particles drifting in a random electric field across a constant magnetic field. The equations o f motion become statistically nonlinear\, and the evolution of dispersion from a short initial ballistic regime\, namely quadratic dependence on tim e\, changes asymptotically to a fractional power law. Accordingly\, the di stribution of particles is not Gaussian\, and the diffusion coefficient ch anges over time. \nThe feature of such a system is that the two-dimensiona l drift of particles occurs along equipotential lines or streamlines. The presence of such an integral of motion allows for dividing the complete en semble of particles into separate groups named subensembles\, which are co ncentrated near streamlines with a certain value of potential. Observation of subensembles allows a better understanding of how the transport occurs as a whole. In this work\, the behavior of the moments of the particle di stribution function was studied using simulation for subensembles with the same initial value of the random potential\, in particular\, the mean squ ared displacement and excess kurtosis were calculated. It is shown that in each subensemble there are particles that travel far from the initial pos ition and that remain close to it. The distribution of the displacement of particles depending on the initial value of the potential was found\, and the average displacements and velocities for the sub-ensembles were calcu lated. It was found that the mean square displacement of the entire ensemb le of particles is formed from the partial contributions. The obtained sta tistical characteristics of particle motion are useful for the verificatio n of analytical models.\n\nhttps://indico.bitp.kiev.ua/event/13/contributi ons/339/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/339/ END:VEVENT BEGIN:VEVENT SUMMARY:Lattice models of ionic liquids in conducting slit nanoconfinement DTSTART;VALUE=DATE-TIME:20240924T132500Z DTEND;VALUE=DATE-TIME:20240924T133000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-378@indico.bitp.kiev.ua DESCRIPTION:Speakers: Maxym Dudka ()\nConfined ionic liquids exhibiting ex citing physics are essential in modern technologies. The narrow conducting confinements cause exponential screening of the electrostatic interaction s between ions\, allowing the development of models with short-range inter actions that can provide analytical insights into the charge storage mecha nisms. In this contribution\, we present a lattice model for ionic liquids confined in ultranarrow slit-shaped pores admitting a single layer of ion s. In the case of next-nearest interactions\, it can be mapped onto the we ll-known three-state Blume-Capel model\, which obeys an analytical solutio n within the Bethe-lattice approximation [1]. Analyzing phase behavior and pore charging in terms of pore ionophilicity\, interionic interactions\, and applied potential difference\, we obtained a phase diagram comprising the lines of first- and second-order\, direct and re-entrant phase transit ions\, manifested by singularities in the capacitance-voltage dependence [ 2]. These analytical results are corroborated by lattice Monte Carlo simul ations [3]. However\, it is known that\, at least in the quasi-one-dimensi onal case of single-file pores\, the results of the lattice model with sho rt-range interactions differ even qualitatively from the exact results of the corresponding continuous model [4]. We will discuss possible ways to improve the lattice model by considering further interactions and analyzin g changes in the phase diagram depending on the interaction parameters.\n\ nThis research is supported by bilatheral project № M/72-2024 between M inistry of Education and Science of Ukraine and Polish National Agency for Academic Exchange (NAWA) as well as U. S. Department of Energy (DOE)\, Of fice of Science\, Basic Energy Sciences\, Materials Science and Engineerin g Division\, under Award No. DE–SC0013599 (Subaward No. UTAUS-SUB0000079 5) \n\n[1] M. Dudka\, S. Kondrat\, A.A. Kornyshev\, G. Oshanin\, J. Phys.: Condens. Matter 28\, 464007 (2016). \n[2] M. Dudka\, S. Kondrat\, O. Beni chou\, A. A. Kornyshev\, G. Oshanin\, J. Chem. Phys. 151\, 184105 (2019).\ n[3] Ya. Groda\, M. Dudka\, A.A. Kornyshev\, G. Oshanin\, S. Kondrat\, J. Phys. Chem. C 125\, 4968 (2021)\n[4] T. Verkholyak\, A.Kuzmak\, S. Kondra t\, J. Chem. Phys. 155\, 174112 (2021)\n\nhttps://indico.bitp.kiev.ua/even t/13/contributions/378/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/378/ END:VEVENT BEGIN:VEVENT SUMMARY:Graph Structural Complexity DTSTART;VALUE=DATE-TIME:20240924T132000Z DTEND;VALUE=DATE-TIME:20240924T132500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-318@indico.bitp.kiev.ua DESCRIPTION:Speakers: Andrei Snarskii (The National Technical University o f Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"\, Dep. of General Phy sics)\nIntroduced the quantitative measure of the structural complexity of the graph (complex network\, etc.) based on a procedure similar to the re normalization process\, considering the difference between actual and aver aged graph structures on different scales. The proposed concept of the gr aph structural complexity corresponds to qualitative comprehension of the complexity. The proposed measure can be obtained for the weighted graphs a lso. \nThe structural complexities for various graph types were found – the deterministic infinite and finite size graphs\, artificial graphs of d ifferent natures including percolation structures\, and the time series of cardiac rhythms mapped to complex networks using the parametric visibilit y graph algorithm. The latter reaches a maximum near the formation of a gi ant component in the graph or at the percolation threshold for 2D and 3D s quare lattices when a giant cluster having a fractal structure has emerged . Therefore\, the graph structural complexity allows us to detect and stu dy the processes similar to a second-order phase transition in complex net works. \nA new node centrality index\, characterizing the structural compl exity of a certain node within the graph structure is introduced also\, it can serve as a good auxiliary or generalization to the local clustering c oefficient. Such an index provides another new ranking manner for the grap h nodes.\nBeing an easily computable measure\, the graph structural comple xity might help to reveal different features of complex systems and proces ses of the real world.\n\nhttps://indico.bitp.kiev.ua/event/13/contributio ns/318/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/318/ END:VEVENT BEGIN:VEVENT SUMMARY:Collapse mitigation in a socioeconomic system under a systemic sho ck DTSTART;VALUE=DATE-TIME:20240924T131500Z DTEND;VALUE=DATE-TIME:20240924T132000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-337@indico.bitp.kiev.ua DESCRIPTION:Speakers: Sergey Lukyanets (Institute of Physics\, National Ac ademy of Sciences of Ukraine)\nSystemic shocks inevitably lead to negative socioeconomic outcomes. The COVID-19 pandemic and the war in Ukraine are the prominent examples of such systemic shocks. Shock-initiated spreading processes often have a domino effect on both the social and economic level s. The war in Ukraine\, despite its devastating effect on the Ukraine’s society and economy\, has not led to the full collapse\, against all odds. In this work\, we make an attempt to provide at least a qualitative illus tration of the mechanisms governing the dynamics of a socioeconomic system in the state of collapse from the viewpoint of statistical physics. Surpr isingly\, we uncover common principles that allow the overall collapsing s cenario to be mitigated\, with the system’s dynamics stabilized. \n\nWe consider a response of a socioeconomic system to a systemic shock in a gro up of economic agents with limited economic resource. To this end\, we exp loit a simple two-level model of active and passive economic agents with m utual negative feedback between the number of active agents and collective resource acquisition [1]. In this case\, economic resource is associated with the average amount of money or income per economic agent and formally corresponds to the effective market temperature\, with the income distrib ution of economic agents obeying the Boltzmann–Gibbs statistics [2]. The coupling between the spreading process and resource in such a system is s upposed to be of activation type\, with the transition rate between the pa ssive and active populations governed by the activation mechanism (Arrheni us-like law). A characteristic level of resource consumption is associated with activation energy (e.g.\, corresponding to the minimum level of reso urce consumption in our particular case).\n\nWe show that the phase portra it of the system features a collapse phase\, in addition to the shock-free and post-shock phases. The shock intensified by the increasing resource d eficit can ultimately drive the system to a collapse at nonzero activation energy because of limited resource – the effect opposite to thermal exp losion. In this case\, the system can no longer stabilize and return to th e stable shock-free state or a poorer post-shock state. We demonstrate tha t there exists a certain critical point at which the system collapses at a ny initial conditions. Moreover\, social regulations in the case of low ec onomic resource can have a negative effect and provoke the system’s coll apse. On the other hand\, there are simple external measures that can prot ect the system against the collapse\, which make the focus of our investig ation. We demonstrate that the system’s collapse can partially be mitiga ted by external subsidies meaning constant resource inflow from some exter nal source or by means of debt interpreted as a negative resource. \n\nIt is interesting that a two-level model considered here formally describes t he dynamics of cooling of a system of agents due to shock-induced transiti ons between two discrete inner states of agents. In this case\, the crisis state of the financial market can be associated with a Bose condensate-li ke state at low market temperature [3]. A more complex multi-level system of interacting agents as well as different interacting social groups can a lso be considered [4].\n\n[1] Gandzha I.S.\, Kliushnichenko O.V.\, Lukyane ts S.P. A toy model for the epidemic-driven collapse in a system with limi ted economic resource. Eur. Phys. J. B 94\, 90 (2021). \nhttps://doi.org/1 0.1140/epjb/s10051-021-00099-7\; https://arxiv.org/abs/2012.12113 \n[2] Ya kovenko V.M.\, Rosser J.B.\, Jr. Colloquium: Statistical mechanics of mone y\, wealth\, and income. Rev. Mod. Phys. 81\, 1703 (2009). https://doi.org /10.1103/RevModPhys.81.1703 \n[3] Kusmartsev F.V. Statistical mechanics of economics I. Phys. Lett. A 375\, 966 (2011).\nhttps://doi.org/10.1016/j.p hysleta.2011.01.003\n[4] Gandzha I.S.\, Kliushnichenko O.V.\, Lukyanets S. P. Modeling and controlling the spread of epidemic with various social and economic scenarios. Chaos\, Solitons & Fractals 148\, 111046 (2021). \nht tps://doi.org/10.1016/j.chaos.2021.111046\n\nhttps://indico.bitp.kiev.ua/e vent/13/contributions/337/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/337/ END:VEVENT BEGIN:VEVENT SUMMARY:On the solution of the problem of the cosmological constant DTSTART;VALUE=DATE-TIME:20240924T131000Z DTEND;VALUE=DATE-TIME:20240924T131500Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-369@indico.bitp.kiev.ua DESCRIPTION:Speakers: Oleksandr Bukalov (Centre for Physical and Space Res earch\, International Institute of Socionics)\nCalculation of the vacuum e nergy density in quantum field theory gives a value $10^{122}$ times highe r than the observed one\, and many proposed approaches have not solved thi s problem and have not calculated its real value. However\, the applicatio n of the microscopic theory of superconductivity to the description of the physical vacuum on the Planck scale made it possible to solve the problem of the cosmological constant and obtain a formula for the observed vacuum density or dark energy. Its numerical value is $6.09 \\cdot 10^{-30} g/cm ^3$\, and it is in complete agreement with observations\, since the experi mental value is $(6.03 ± 0.13) \\cdot 10^{-30} g/cm^3$ (J. Prat\, C. Hoga n\, C. Chang\, J. Frieman\, 2022).\nThe cosmological model with supercondu ctivity (CMS)\, proposed by the author\, also implies a description of the earliest stage of the Universe evolution preceding the inflation stage. I t describes the formation of the inflaton field as a special condensate of primordial fermions with the Planck mass\, followed by the inflationary e xpansion of the early Universe. The current expansion of the Universe and its evolution are described as an ongoing second-order phase transition\, and the flow of physical cosmological time is a consequence of processes o ccurring on Planck scales. The value of the Hubble parameter $H_0=69.76 \\ km \\cdot s^{-1}Mpc^{-1}$ calculated in CMS corresponds to the average va lue for most values of this parameter obtained by different methods. CMS a lso describes black holes as a quantum condensate of primary fermions with Planck mass.\n\nReferences:\n\n 1. Weinberg\, S.\, “The cosmological co nstant problem”\, Reviews of Modern Physics\, vol. 61\, no. 1\, APS\, pp . 1–23\, 1989. doi:10.1103/RevModPhys.61.1.\n 2. Bukalov\, A. V.\, “Th e Solution of the Cosmological Constant Problem and the Formation of the S pace-Time Continuum”\, Odessa Astronomical Publications\, vol. 29\, p. 4 2\, 2016. doi:10.18524/1810-4215.2016.29.84962.\n 3. Pitaevskii\, L. P.\, Lifshitz\, E. M. Statistical Physics Part 2 (1980).\n 4. Fomin\, P. I.\, “Zero cosmological constant and Planck scales phenomenology”\, Proc. o f the Fourth Seminar on Quantum Gravity\, May 25–29\, Moskow / Ed. by M. A.Markov. — Singapore: World Scientific\, 1988. — P. 813.\n 5. Fomin\, P. I.\, “On the crystal-like structure of physical vacuum at Planck dis tances”\, Problems of physical kinetics and solid state physics. Kyiv: N aukova dumka\, 1990. — P. 387–398.\n 6. Bukalov\, A. V.\, “On solvin g the problem of the cosmological constant”\, Proceedings of 12-th Odess a International Astronomical Gamow Conference-School “Astronomy and Beyo nd: Astrophysics\, Cosmology and Gravitation\, Cosmomicrophysics\, Radio-a stronomy and Astrobiology” 20-26 August\, 2012\, Odessa\, Ukraine. — P . 28.\n 7. Prat\, J.\, Hogan\, C.\, Chang\, C.\, and Frieman\, J.\, “Vac uum energy density measured from cosmological data”\, Journal of Cosmolo gy and Astroparticle Physics\, vol. 2022\, no. 6\, IOP\, 2022. doi:10.1088 /1475-7516/2022/06/015. arXiv:2111.08151.\n\nhttps://indico.bitp.kiev.ua/e vent/13/contributions/369/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/369/ END:VEVENT BEGIN:VEVENT SUMMARY:Conference opening DTSTART;VALUE=DATE-TIME:20240924T070000Z DTEND;VALUE=DATE-TIME:20240924T072000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-403@indico.bitp.kiev.ua DESCRIPTION:Speakers: Anatoly Zagorodny (NAS of Ukraine)\nhttps://indico.b itp.kiev.ua/event/13/contributions/403/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/403/ END:VEVENT BEGIN:VEVENT SUMMARY:General hydrodynamic approach for a cold Bose gas DTSTART;VALUE=DATE-TIME:20240924T123000Z DTEND;VALUE=DATE-TIME:20240924T125000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-329@indico.bitp.kiev.ua DESCRIPTION:Speakers: Victor Pergamenshchik (Institute of Physics\, NANU\, Kyiv\, Ukraine & Center for Theoretical Physics\, PAN\, Warsaw\, Poland)\ nThe aim of this paper is to derive the hydrodynamics for a cold Bose gas from the microscopic platform based on the many-body Schr¨odinger equatio n and general assumptions of the hydrodynamic approach (HA) applicable to any dimension. We develop a general HA for a cold spatially inhomogeneous Bose gas assuming two different temporal and spatial scales and obtain the energy as a functional of both fast inner quantum mode and slow macroscop ic mode. The equations governing the fast and slow modes are obtained from this functional by their independent variations. The fast mode is the wav e function in the stationary state at local density which can be ground\, excited with a nonzero atom momenta\, or a superposition of more than one states. The energy eigenvalue (or expectation value) of this local wave fu nction universally enters the hydrodynamic equation for the slow mode in t he form of the local chemical potential which incorporates the inner local momentum. For zero inner momenta and particular choices of this eigenvalu e as a function of gas density\, this equation reduces to the known equati ons based on the local density approximation. If however the inner momenta are nonzero\, the equation includes the interaction between these momenta and the slow mode velocity. Relation between this general HA and the stan dard local density approximation is elaborated. Two effects of the local m omenta and their density dependence on the soliton solutions are demonstra ted.\n(To appear in the Physical Review A\, arXiv:2408.12363v1).\n\nhttps: //indico.bitp.kiev.ua/event/13/contributions/329/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/329/ END:VEVENT BEGIN:VEVENT SUMMARY:Effects of metallic and molecular counterions in structural dynami cs of the DNA double helix DTSTART;VALUE=DATE-TIME:20240924T121000Z DTEND;VALUE=DATE-TIME:20240924T123000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-332@indico.bitp.kiev.ua DESCRIPTION:Speakers: Sergiy Perepelytsya (Bogolyubov Institute for Theore tical Physics of the NAS of Ukraine)\nThe structure of the DNA double heli x is stabilized by water molecules and positively charged metallic or mole cular ions\, which form an ion-hydration shell around the macromolecule. T he ions neutralize the negatively charged phosphate groups of the DNA back bone and thus act as counterions. Despite the extensive number of experime ntal and theoretical studies\, the specific effects of counterions on the structural dynamics of the DNA double helix and its ion-hydration shell re main incompletely understood. This contribution will overview the most rec ent findings on this topic based on molecular dynamics simulation results. Specifically\, the effects of hydration of Li$^+$\, Na$^+$\, K$^+$\, Rb$^ +$\, Cs$^+$ and Mg$^{2+}$ counterions localized in different regions of th e DNA macromolecule will be discussed\, along with the interplay of water molecules around the ions and within the hydration shell of the double hel ix [1\,2]. In the case of molecular ions\, the role of conformational effe cts of flexible polyamines (putrescine$^{2+}$\, spermidine$^{3+}$\, and sp ermine$^{4+}$) for the interaction with the DNA double helix and the forma tion of stable DNA-DNA contacts will be described [3-6]. The results will be discussed in the context of understanding the physical mechanisms behin d DNA's biological functioning and the development of DNA-based materials for nanotechnological applications.\n\n[1] Perepelytsya\, S. J. Mol. Model . 2018\, 24 (7)\, 171. https://doi.org/10.1007/s00894-018-3704-x.\n\n[2] P erepelytsya\, S. M. Ukr. J. Phys. 2020\, 65 (6)\, 510. https://doi.org/10. 15407/ujpe65.6.510.\n\n[3] Perepelytsya\, S.\; Uličný\, J.\; Laaksonen\, A.\; Mocci\, F. Nucleic Acids Res. 2019\, 47 (12)\, 6084–6097. https:// doi.org/10.1093/nar/gkz434.\n\n[4] Mocci\, F.\; Laaksonen\, A.\; Engelbrec ht\, L.\; Vasiliu\, T.\; Perepelytsya\, S. In Soft Matter Systems for Biom edical Applications. Springer Proceedings in Physics\, vol 266\; Springer\ , Cham.\, 2022\; pp 163–192. https://doi.org/10.1007/978-3-030-80924-9_6 .\n\n[5] Vasiliu\, T.\; Mocci\, F.\; Laaksonen\, A.\; Engelbrecht\, L. D. V.\; Perepelytsya\, S. M. Front. Chem. 2022\, 10 (February)\, 836994. http s://doi.org/10.3389/fchem.2022.836994.\n\n[6] Perepelytsya\, S.\; Vasiliu\ , T.\; Laaksonen\, A.\; Engelbrecht\, L. D. V.\; Mocci\, F. Low Temperatur e Physics 2024\, 50 (3)\, 204–214. https://doi.org/10.1063/10.0024969.\n \nhttps://indico.bitp.kiev.ua/event/13/contributions/332/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/332/ END:VEVENT BEGIN:VEVENT SUMMARY:Methods of Neutron Optics fof Studying Physical Properties of Liqu ids DTSTART;VALUE=DATE-TIME:20240924T113000Z DTEND;VALUE=DATE-TIME:20240924T121000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-324@indico.bitp.kiev.ua DESCRIPTION:Speakers: O. V. Chalyi (Department of Medical and Biological P hysics and Informatics\, O. O. Bogomolets National Medical University\, Ky iv\, Ukraine)\nThis presentation is aimed at using neutron optics methods to study the physical properties of bulk and confined liquids. To achieve this goal\, the defining idea of M.M. Bogolyubov regarding the hierarchy o f relaxation times and the sequential description of the dynamic evolution of condensed systems was used [1]. The following results were obtained by the methods of neutron optics [2-6]\, which apply the Schrödinger equati on for the neutron wave function and the Fermi potential depending on the local numerical value of the density of nuclei [2]:\n1. For bulk liquids\, the singular behavior of the temperature derivative for the diameter of t he neutron refractive index (NRI) is theoretically predicted\, the main re ason for which is a violation of the Polyakov conformal invariance hypothe sis on the coexistence curve of a real liquid-vapor system.\n2. Due to the spatial inhomogeneity of the bulk fluid near the critical state in the ex ternal gravitational field (see\, for example\, [7\,8])\, the appearance o f a uniaxial ellipsoid of the NRI has been proven (by analogy with the ell ipsoid of wave normals in crystal optics). The parameters of such an ellip soid were determined for a cylindrical volume of liquid with a radius sign ificantly larger than the correlation length of density fluctuations. On t he axis of such a cylindrical sample\, the uniaxial NRI ellipsoid becomes the NRI sphere.\n3. Different signs of the coherent scattering length of t he components of the solution of liquids predict the phenomenon of zero re fraction of the neutron beam\, which resembles the zero optical activity o f a racemic mixture. Theoretical calculations established that for a binar y solution of ethane and carbon dioxide\, the phenomenon of zero refractio n of the neutron beam should take place in the solution of [6].\n4. It was theoretically established that the temperature dependence of the peak wid th of quasi-elastic scattering of slow neutrons is quantitatively confirme d by experimental results for confined supercooled water with spatial dim ension d = 2 near its lower critical temperature T = 2280С [9].\n5. Using Mandelbrot's formula [10] for the fractal dimension\, it was proved that the dependence of the cross section of the elastic neutron scattering\, be ing proportional to the random mean-square fluctuation of the number densi ty of nuclei\, on linear sizes of a confined liquid volume is determined b y a new critical index\, which is equal to the fractal dimension. For syst ems that belong to the universality class of the Ising model in a magnetic field\, the fractal dimension values are 1.875 and 2.482\, respectively\, for spatial dimensions d = 2 and d = 3 [11].\n6. It has been proven that the method of quasi-elastic neutron scattering [4\,6] makes it possible to create a reliable basis for new diagnostic tests of the carcinogenesis pr ocess based on the established correlation between the self-diffusion coef ficient of water molecules in aqueous suspensions of plasma membranes and the sensitivity of different groups of tissues to anticancer drugs [12]. A nother biomedical application of neutron optics methods is the calculation of NRI and refraction of a neutron beam in an aqueous suspension of prote ins and lipids.\n\n1. М.М. Bogolyubov. Problems of Dynamic Theory in Sta tistical Physics. Naukova Dumka\, Kyiv\, 1970\n2. Enrico Fermi. Collected Paper: (Note e memorie)\, v.1. Italy 1921-1938\; v.2. United States 1939-1 954\; University of Chicago Press\, Chicago\, 1964. \n3. I.M. Frank\, Neut ron optics and ultracold neutrons\, Phys. Sci. Advances 161(11): 109-127\, 1991.\n4. L.A. Bulavin\, K.O. Chalyy. Neutron Optics of Mesoscale Liquids . Naukova Dumka\, Kyiv\, 2006.\n5. V.I. Sygakov\, О.V. Chalyi\, L.М. Che rnenko. Critical neutron opalescence in a heterogeneous liquid. 1. Ukr. J. Phys. 35(7): 1036-1941\, 1990\; 2. Ukr. J. Phys. 36(9) 1355-1362\, 1991.\ n6. A.V. Chalyi\, L.A. Bulavin\, K.A. Chalyy. On the neutron optics of liq uids. J. Mol. Liquids 383: 121979\, 2023.\n7. M.E. Fisher. The theory of c ritical point singularities. In M.S. Green (Ed.) Critical Phenomena. Inter n. School Phys. “Enrico Fermi”\, Acad. Press\, New York\, 1971.\n8. K. A. Chalyy\, K. Hamano\, A.V. Chalyi. Correlating properties of a simple li quid at criticality in a reduced geometry. J. Mol. Liquids 92 (1-2) 153-16 4\, 2001. \n9. A.V. Chalyi. Dynamic anomalies in confined supercooled wate r and bulk fluids. In L.A. Bulavin and A.V. Chalyi (Eds.) Modern Problems of Molecular Physics\, Springer\, 253-290\, 2018.\n10. B. Mandelbrot. The Fractal Geometry of Nature. W.H. Freeman and Company\, New York\, 1982.\n1 1. A.V. Chalyi. Effective fractal dimension at 2d – 3d crossover. Fracta l and Fractional 6: 739-750\, 2022.\n12. L.A. Bulavin\, V.F. Chekhun\, O.A \, Vasilkevych\, V.I. Kovalchuk\, V.T. Krotenko\, V.I. Slisenko\, V.P. Tr yndyak\, K.O. Chalyy. Neutron studies of self-diffusion of water molecules in plasma membranes. J. Phys. Studies 8(4):334-337\, 2004.\n\nhttps://ind ico.bitp.kiev.ua/event/13/contributions/324/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/324/ END:VEVENT BEGIN:VEVENT SUMMARY:Entanglement of the diamond spin cluster DTSTART;VALUE=DATE-TIME:20240924T101000Z DTEND;VALUE=DATE-TIME:20240924T103000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-341@indico.bitp.kiev.ua DESCRIPTION:Speakers: Andrij Kuzmak (Professor Ivan Vakarchuk Department f or Theoretical Physics\, Ivan Franko National University of Lviv)\nThe ent anglement of diamond spin systems in thermodynamic equilibrium has\nbeen s tudied in various papers (for\, example\, [1\, 2\, 3\, 4]). We focus on th e evolution of entanglement in a diamond spin-1/2 cluster. This cluster co nsists of two central spins described by the anisotropic Heisenberg model\ , which interact with two side spins via an Ising interaction. The influen ce of the interaction coupling with the side spins on the entanglement of the central spins is investigated [5\, 6]. It is demonstrated that the beh avior of entanglement between the central spins can be controlled by choos ing the appropriate value of this coupling. Additionally\, we examine the influence of a bosonic bath on the entanglement of the central spins.\n\nR eferences\n[1] I. Bose\, A. Tribedi\, Phys. Rev. A 72\, 022314 (2005).\n[2 ] A. Tribedi\, S. Bose\, Phys. Rev. A 74\, 012314 (2006).\n[3] O. Rojas\, M. Rojas\, S. M. de Souza\, J. Torrico\, J. Strecka\, M. L. Lyra\, Physica \nA 486\, 367 (2017).\n[4] A. Ghannadan\, KatarГңna Karl’ova\, J. Stre cka\, Magnetochemistry 8\, 11\n(2022).\n[5] A. R. Kuzmak\, J. Phys. A 56\, 165302 (2023).\n[6] A. R. Kuzmak\, Ann. Phys. (NY) 455\, 169397 (2023).\n \nhttps://indico.bitp.kiev.ua/event/13/contributions/341/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/341/ END:VEVENT BEGIN:VEVENT SUMMARY:Cubic-quintic interplay in the nonlinear Klein–Gordon model DTSTART;VALUE=DATE-TIME:20240924T095000Z DTEND;VALUE=DATE-TIME:20240924T101000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-311@indico.bitp.kiev.ua DESCRIPTION:Speakers: Ivan Gandzha (Institute of Physics\, National Academ y of Sciences of Ukraine)\nThe nonlinear Klein–Gordon (nKG) model\,\n$\n \\partial_{tt}\\phi-c^{2}\\partial_{xx}\\phi+f(\\phi)=0\,\n$ \n is a unive rsal model for describing the propagation of nonlinear waves in various ph ysical media. For example\, its stationary version describes the macroscop ic wave function of the condensed phase (i.e.\, the order parameter) in th e Landau theory of phase transitions. Noteworthy is also an application of the nKG model to modelling the spatially localised oscillating excitation s of biological structures such as DNA chains. Here\, the unknown real fun ction $\\phi$ is a characteristic of the wave field\, $t$ is time\, $x$ is coordinate\, $c$ is the velocity parameter that deals with the speed of i nteraction propagation. The function $f$ is a nonlinear function of the wa ve field that describes the nonlinear response of the medium.\n\nIn this w ork\, we are interested in the interplay between the cubic and quintic ter ms of the nonlinear response function\, which we present as a truncated po lynomial (corresponding to a $\\phi^6$ field model)\, \n$\nf(\\phi)=\\alph a_1\\phi+\\alpha_{3}\\phi^{3}+\\alpha_{5}\\phi^{5}.\n$ \n The real coeffic ient $\\alpha_{1}$ describes the linear response of the medium. The real c oefficients $\\alpha_{3}$ and $\\alpha_{5}$ represent the cubic and quinti c nonlinearities\, respectively. \n\nBy reducing the nKG model to an exten ded cubic-quintic nonlinear Schrödinger equation in Hamiltonian form\, we demonstrate that the quintic nonlinearity has a profound effect on the st ability of wave packets to long-wave modulations. When there is no quintic nonlinearity ($\\phi^4$ field model)\, plain wave packets in such a syste m are known to be modulationally unstable for any carrier wave number in t he case of negative coefficient at cubic nonlinearity. We show that such p lain wave packets become modulationally stable for certain carrier wave nu mbers when the quintic nonlinearity becomes large enough. Such a stabilisa tion of the wave packet happens at certain critical ratio between the quin tic and cubic coefficients of the nKG model.\n\nThis work proves that high -order nonlinear effects may play a decisive role in analysing physical ph enomena in nonlinear models at certain conditions. This result may have pr actical implications for nonlinear media that exhibit the generation of hi gher harmonics and are characterised by a significant quintic nonlinearity (e.g\, in polarisation). In particular\, such conditions are met for ferr oelectrics with first-order phase transition (e.g.\, BaTiO$_3$ crystals).\ n\nPublications:\n\n1. Sedletsky Yu.V.\, Gandzha I.S. Hamiltonian form of extended cubic-quintic nonlinear Schrödinger equation in a nonlinear Klei n-Gordon model. Phys. Rev. E 106\, 064212 (2022). https://doi.org/10.1103/ PhysRevE.106.064212\n\n2. Sedletsky Yu.V.\, Gandzha I.S. Fifth-order nonli near Schrödinger equation as Routhian reduction of the nonlinear Klein– Gordon model. Proc. R. Soc. A 479\, 20230315 (2023). https://doi.org/10.10 98/rspa.2023.0315\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/31 1/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/311/ END:VEVENT BEGIN:VEVENT SUMMARY:To 190 years of the Wave of Translation and 50 years of the Davydo v's soliton: Soliton dynamics in an oscillating magnetic field. DTSTART;VALUE=DATE-TIME:20240924T093000Z DTEND;VALUE=DATE-TIME:20240924T095000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-313@indico.bitp.kiev.ua DESCRIPTION:Speakers: Larissa Brizhik (Boglyubov Institute fr Theoretical Physics)\nIn this talk some less known facts of the discovery of the Wave of Translation will be discussed. A brief review of the advancement of the theory of Davydov's solitons will be given. New results on the study of t he dynamics of the Davydov’s soliton [1] in an external oscillating in t ime magnetic field [2\,3] will be reported.\n It is shown that in the magn etic field\, perpendicular to the molecular chain axis\, soliton wave func tion is a superposition of the electron plane wave in the plane perpendicu lar to the molecular chain\, and longitudinal component of the wave functi on which satisfies the modified Nonlinear Schroedinger equation which is s olved using the perturbation method based on the inverse scattering transf orm. It is shown that soliton width and amplitude are constant\, while its velocity and phase are oscillating in time functions with the frequency o f the main harmonic determined by the magnetic field frequency. Account of the energy dissipation results in bounding soliton velocity from above d ue to the balance of the energy gain from the magnetic field\, and its los s because of the radiation of linear sound waves and energy dissipation. S oliton radiation due to time-depending velocity is calculated and shown to be the most intensive at the resonant frequency of the magnetic field. It is concluded that such complex impact of time-depending magnetic fields o n charge transport\, provided by solitons\, can affect functioning of the devices based on low-dimensional molecular systems. These results suggest the physical mechanism of the resonant therapeutic effects of oscillating magnetic fields as the resonant impact of the magnetic field on the charge transport processes provided by solitons in the redox processes [4\,5].\n \nAcknowledgement: \nThis work was supported by the fundamental scientific program 0122U000887 of the Department of Physics and Astronomy of the Nat ional Academy of Sciences of Ukraine. The author acknowledges the Simons F oundation (NY).\n\n[1] A.S. Davydov\, N.I. Kislukha. Solitary excitons in one-dimensional molecular chains. Phys. Stat. Sol. B (1973) **5** 465. ht tps://doi.org/10.1002/pssb.2220590212\n[2] L. Brizhik. Davydov’s soliton in an external alternating magnetic field. arXiv:2402.09172v1 [cond-mat.s oft] 14 Feb 2024.\n[3] L. Brizhik. Dynamics of the Davydov's soliton in ex ternal oscillating magnetic field (Submitted to Chaos\, Solitons and Fract als\, 2024).\n[4] L. Brizhik\, E. Fermi\, B. Zavan. Working principle of m agnetic resonance therapy. http://arxiv.org/abs/1509.04475\n[5] Electric\, Magnetic\, and Electromagnetic Fields in Biology and Medicine: From Mecha nisms to Biomedical Applications: 2nd Edition. Bioengineering\, Special Is sue. (2024)\, **11**.\n\nhttps://indico.bitp.kiev.ua/event/13/contribution s/313/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/313/ END:VEVENT BEGIN:VEVENT SUMMARY:Properties of multi-qubit states representing directed graphs and their studies with quantum programming DTSTART;VALUE=DATE-TIME:20240924T084000Z DTEND;VALUE=DATE-TIME:20240924T090000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-322@indico.bitp.kiev.ua DESCRIPTION:Speakers: Khrystyna Gnatenko (Ivan Franko National University of Lviv)\nWe analyze multi-qubit states that can be represented using dire cted graphs G(V\,E). We focus on the geometric properties of these states\ , namely on curvature and torsion [1]. It has been found that the curvatur e of quantum states is determined by the sum of the weighted degrees of no des in graphs where the weights in G(V\,E) are raised to the second and fo urth powers [2]. Additionally\, curvature depends on the sum of the produc ts of the weights of edges that form squares within the graph G(V\,E). The torsion\, on the other hand\, is connected to the sum of the products of the weights of edges that create triangles in the graph G(V\,E). We have c omputed these geometric properties on IBM's quantum computer in the case o f a quantum graph state corresponding to a chain [2].\nWe have also exami ned quantum states that represent directed networks. We calculated the ent anglement of these states both analytically and by programming on AerSimul ator. We identified relationships between the geometric measure of entangl ement and the weights of incoming and outgoing arcs\, the outdegree\, and indegree of the vertex corresponding to the qubit in the graph [3].\n\n \n [1] H. P. Laba\, V. M. Tkachuk\, Condens. Matter Phys. 20\, 13003 (2017).\ n[2] Kh. P. Gnatenko Relation of curvature and torsion of weighted graph s tates with graph properties and its studies on a quantum computer\, arXiv: 2408.01511 (2024).\n[3] Kh. P. Gnatenko Physics Letters A 521\, 129815 (2 024)\n\nhttps://indico.bitp.kiev.ua/event/13/contributions/322/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/322/ END:VEVENT BEGIN:VEVENT SUMMARY:Reading Ernst Ising’s dissertation hundred years on DTSTART;VALUE=DATE-TIME:20240924T080000Z DTEND;VALUE=DATE-TIME:20240924T084000Z DTSTAMP;VALUE=DATE-TIME:20260518T022327Z UID:indico-contribution-13-315@indico.bitp.kiev.ua DESCRIPTION:Speakers: Yurij Holovatch (ICMP NASU\, Lviv)\nThe Ising model is an archetype describing collective ordering processes. As such\, it is widely known in physics and far beyond. Less known is the fact that the th esis defended by Ernst Ising 100 years ago under supervision of Wilhelm Le nz [1] contained not only the solution of what we call now the ‘classica l 1D Ising model’ but also other problems. Some of these problems are th e subject of this report [2\,3]. In particular\, I will discuss (i) a mode l proposed in 1922 by Walter Schottky and its relation to the Ising model [2]\; (ii) the combinatorial method Ernst Ising used to calculate the part ition function for a chain of elementary magnets [3]\; (iii) the generaliz ations of the two-state model suggested in Ernst Ising’s thesis but not exposed in his paper [3]. The talk is a part of an ongoing project that ai ms to prepare a bilingual\, commented edition of the doctoral thesis of Er nst Ising [4].\n\n[1]. Beitrag zur Theorie des Ferro- und Paramagnetismus. Dissertation zur Erlangung der Doktorwürde der Mathematisch–Naturwisse nschaftlichen Fakultät der Hamburgischen Universität vorgelegt von Ernst Ising aus Bochum. Hamburg 1924\; E. Ising. Beitrag zur Theorie des Ferrom agnetismus. Zeitschr. f. Phys. 31 (1925) 253–258.\n\n[2]. R. Folk\, Yu.. Holovatch. Schottky's forgotten step to the Ising model. Eur. J. Phys. H 47 (2022) 9.\n\n[3]. R. Folk\, Yu. Holovatch. Ising's roots and the transf er-matrix eigenvalues. Entropy 26(6) (2024) 459.\n\n[4]. B. Berche\, R. Fo lk\, Yu. Holovatch\, R. Kenna\, in preparation\n\nhttps://indico.bitp.kiev .ua/event/13/contributions/315/ LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst itute of Mathematics (Section 5) 322 URL:https://indico.bitp.kiev.ua/event/13/contributions/315/ END:VEVENT END:VCALENDAR