Nuclear deflagration phenomenon and prospective concept of safe fast breeder reactor (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Sergii Fomin (AITP NSC KIPT)

Room: Conference Hall This review discusses the physical nature and conditions governing the phenomenon of slow nuclear burning in a breeding medium - “nuclear deflagration”- specifically in the breeding zone of a fast breeder reactor. A brief overview is provided of various theoretical approaches to describing this phenomenon and the results obtained based on them [1–4]. The results of our study of the nuclear deflagration in the form of nuclear burning wave are presented. This study is based on an original deterministic approach that relies on the numerical solution of a non-stationary, nonlinear, multi-group neutron diffusion equation in conjunction with a system of fuel nuclide burnup equations and equations of nuclear kinetics of precursors of delayed neutrons [5–7]. The unique “intrinsic safety” properties and other advantages of a promising fast breeder reactor operating in a nuclear burning wave mode are discussed; the main parameters of such a reactor are presented; and problematic issues and possible solutions are addressed. The research is part of the TREASURE coordinated research project under the EURATOM program (Project No. 101164616), which is being carried out from 2024 to 2028. 1. L.P. Feoktistov. Preprint IAE-4605-4, 1988; Sov. Phys. Doklady, 34 (1989) 1071. 2. V.Ya. Gol’din and D.Y. Anistratov. Sov. Journ. Mathematical Modeling, 7:10 (1995) 12. 3. E. Teller. Nuclear Energy for the Third Millennium. Preprint UCRL-JC-129547, LLNL, 1997. 4. H. Sekimoto, K. Ryu, Y. Yoshimura. Nuclear Science and Engineering, 139 (2001) 306. 5. S.P. Fomin et al. Annals of Nuclear Energy, 32 (2005) 1435; 148 (2020) 107699. 6. S.P. Fomin et al. Progress in Nuclear Energy, 50 (2008) 163; 53 (2011) 800. 7. S.P. Fomin et al. Proc. Intern. Conf. on Fast Reactors & Related Fuel Cycle, Paris, France, 2013, paper CN-199-457; Vienna, Austria, 2022, paper CN-291-365.

Quasi-Linkage Equilibrium in spatially separated populations and in diploid genetics (STATISTICAL PHYSICS AND SOFT MATTER)

• Erik Aurell (Department of Computational Science and Technology, KTH-Royal Institute of Technology, AlbaNova University Center)

Room: Conference Hall Quasi-Linkage Equilibrium (QLE) is a theory developed by Kimura (1965) and Neher & Shraiman (2009:2011) to explain the emergency of distributions of genotypes in a population akin to the canonical ensemble in statistical physics, referred to as a QLE state. Recombination (exchange of genetic material between individuals) acts analogously to molecular collisions in kinetic gas theory, and leads, if strong enough, to relaxation to an equilibrium-like state, for a review, see [1]. Geographic isolation is important in evolution, it is a driving force behind speciation. I will discuss how recombination interacts with migration between spatially isolated sub-populations, and if the QLE state can coexist with migration. I will also consider the setting where different sub-populations live in different environments with different fitness landscapes, and if one can infer those landscapes from the population structures if individuals can move between the populations [2]. I will also discuss the conceptual issue if the assumption of haploid genomes usually made in the literature is only a simplification or if the evolution of diploid populations is qualitatively different and can lead to other phases than QLE. [1] "Statistical genetics in and out of quasi-linkage equilibrium", V Dichio, HL Zeng, E Aurell, Reports on Progress in Physics 86 (5), 052601 (2023) [2] "Fitness Inference in Presence of Migrations between Coupled Evolving Populations", YH Huang, B Dumont, HL Zeng, J Barton, E Aurell (2026), arXiv preprint arXiv:2605.22665

Criticality of structurally-disordered spin systems with weak long-range interactions (STATISTICAL PHYSICS AND SOFT MATTER)

• Maxym Dudka (Yukhnovskii Institute of Condensed Matter Physics, National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine; ${\mathbb L}^4$ Collaboration \& Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, Europe; Lviv Polytechnic National University 79013 Lviv, Ukraine)

Room: Conference Hall Studies of low-temperature ordering in long-range interacting many-particle systems continue to attract significant interest. While such systems are common in nature, some features of their critical behavior remain unexplained. We address the combined impact of weak structural disorder and weak long-range interactions decaying in $d$-dimensional space as $x^{-d-\sigma}$ with $\sigma > 0$ on the critical behavior of classical model with $n$-component spins. Whithin specific regions of the parameter space $(n, d, \sigma)$, this model exibits a distinct disorder-induced long-range universality class. To characterize this universality class we calculate the marginal dimensions [1] and scaling exponents [2,3] governing the system's criticality within the three-loop approximation of field-theoretical renormalization group approach. Furthermore, we present refined estimates of these universal quantities by applying resummation techniques to the divergent perturbation series. M.D. and D.S. acknowledge support of the U. S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science and Engineering Division, under Award No. DE–SC0013599 [1] D. Shapoval, M. Dudka, Yu. Holovatch, *Low Temp. Phys.* $\textbf{48}$ (2022) 1049. [2] M. Dudka, D. Shapoval, Yu. Holovatch, *Journal of Physical Studies* $\textbf{28}$ (2024) 2601. [3] D. Shapoval, M. Dudka, *Condens. Matter Phys.* $\textbf{28}$ (2025) 43503.

Stabilizing role of the dissipation effects in the dynamics of electrosolitons in magnetic field (CONDENSED MATTER PHYSICS)

• Larissa Brizhik (Boglyubov Institute fr Theoretical Physics)

Room: Conference Hall Analytical [1] and numerical [2] study of the magnetic field impact on the dynamics of electrosolitons, i.e., charged Davydovs solitons, in one-dimensional systems has shown that in the presence of the field soliton velocity and acceleration attains oscillations with the frequency determined by the field. It has been shown that the impact of a magnetic field within both approaches depends not only on the field strength, but also on the parameter values of the system which define such properties of polarons like their energy, amplitude, width of localization. Because of the non-zero acceleration soliton velocity gradually increases with time and at large times soliton starts to radiate linear sound and electromagnetic waves due to which soliton loses its energy and becomes less stable. Nevertheless, in real situations there are always present dissipative effects. Molecular chains interact with the surrounding, electron itself interacts not only with the acoustical phonons, but with other vibrational modes, etc., so that the energy dissipation has to be taken into account. It is shown that it can be done by adding an additional term into the corresponding equations of motion. In the continuum model soliton dynamics in the magnetic field is governed by the Modified Cubic Nonlinear Schoedinger Equation with two extra terms determined by the presence of the magnetic field and energy dissipation. Both extra terms are small. The equation is solved using the nonlinear perturbation method. It is shown that with increasing soliton velocity due to magnetic field energy dissipation increases and as a result, soliton acceleration decreases and its dynamics is stabilized. The obtained results demonstrate that soliton dynamics remains stable even in relatively strong magnetic fields. Therefore, solitons can provide effective long-range electron transport in biological systems and novel low-dimensional functional materials used in modern nano- and biotechnologies. Acknowledgment This work was done in frame of the project of the National Academy of Sciences of Ukraine “Properties of low-dimensional materials in the presence of external perturbations, structural defects and topological states”, registration number 0122U000887 [1] L. Brizhik. Chaos, Sol. Fractals 187 (2024) 115459 https://doi.org/10.1016/j.chaos.2024.115459. [2] L. Brizhik B.M.G. Piette, Chaos, Sol. Fractals 208 (2026) 118339 https://doi.org/10.1016/j.chaos.2026.118339

Associative approach in soft matter theory (STATISTICAL PHYSICS AND SOFT MATTER)

• Myroslav Holovko (Yukhnovskii Institute for Condensed Matter Physics of NAS of Ukraine)

Room: Conference Hall We analyse the possibility of the application of the statistical-mechanical approaches developed in the modern theory of associative fluids for the description of associative phenomena on different properties in soft matter theory [1]. In developed theoretical formalism, the potentials of intermolecular interactions are split into three parts. One of them is the short-range repulsive part responsible for excluded volume effects by molecules. The second one is the short-range strongly attractive part responsible for different clusterization effects, including self-assembly phenomena. The third part is long-range and responsible for the screening and renormalization phenomena. The specificity of the developed approach are connected with the application of the activity diagram expansions for the description of the short-range attractive part of interactions and the density diagram expansions for the description of the last two parts of interactions. Classification and reduction of the obtained diagrams in such expansions leads to the multidensity formalism, whose specificity strongly depends on types of described clusterization phenomena. Special attention is focused on the application of the associative approach in the theory of ionic solutions. The analytical solution of the associative mean spherical approximation (AMSA) and the modified version of the mean spherical approximation - the mass action law (MSA-MAL) approach are used to revise the concept of ion association in the theory of electrolyte solutions. It is shown that AMSA theory is more preferable for the description of thermodynamical properties while the modified version of the MSA-MAL theory is more useful for the description electrical properties [2]. The proposed theory is applied to explain the anomalous properties of the electrical double layer in a low temperature region and for the treatment of the effect of electrolyte on the rate of intermolecular electron transfer. We applied the developed approach for the description of solubilization of biological molecules in reverse micellar systems and the study of biomolecules' influence on the properties of considered systems. As an example, we consider solubilization of cytochrome-c in water in oil reverse micellar system [3] and the solubilization of RNA in water in reverse wormlike micellar systems with lipid covering. The associative approach also gives the possibility to construct the macromolecular systems from chemical functional groups.

Whether the Hypothesis of Conformal Invariance Is Fulfilled Near the Critical Points of Fluids? (STATISTICAL PHYSICS AND SOFT MATTER)

• A.V. Chalyi (Bogomolets National Medical University)

Room: Conference Hall L.A. Bulavin$^{1,2}$, E.G. Rudnikov$^{1,3}$, K.O. Cherevko$^{1,2}$, A.V. Chalyi$^4$ 1 Department of Molecular Physics, Faculty of Physics, Kyiv National Taras Shevchenko University, Volodymyrska Str., 64 Kyiv 01601, Ukraine 2 Institute for Safety Problems of Nuclear Power Plants of the NAS of Ukraine, Lysohirska Street, 12, Kyiv 03028, Ukraine 3 Department of Biomedical Cybernetics, Faculty of Biomedical Engineering, National Technical University of Ukraine "Ihor Sikorsky Kyiv Polytechnic Institute", Beresteyskiy Ave., 37 Kyiv 03056, Ukraine 4 Department of Medical and Biological Physics and Informatics, Bogomolets National Medical University, Shevchenko Blvd., 13, Kyiv 01601, Ukraine Conformal transformations were introduced in the physics of phase transitions by A.M. Polyakov [1]. Based on the hypothesis of conformal invariance (CI), scale invariance with anomalous dimensions was proposed [2], both in the theory of critical phenomena for fluctuating quantities and in hadronic interactions. The CI hypothesis also proves to be fundamental in interdisciplinary research, for example, to explain the formation of hexagonal structures in the system of grid cells in the brain (2014 Nobel Prize in Physiology and medicine) [3] An important consequence of CI hypothesis in the physics of phase transitions, according to [4], is the orthogonality relation for two fluctuating quantities of transitions with different scale dimensions within the algebra of fluctuating quantities, which was proposed by V.L. Pokrovskii [5] (see also [6]). The aim of this work is to verify for the first time the CI hypothesis for the liquid-vapor critical points of single-component fluids based on existing experimental data. For this purpose, we used experimental data for carbon dioxide [7], water [8,9], and polyol ester (POE9) lubricant with a higher critical temperature, for which experimental data are available in the scientific literature [10]. These fluids have critical temperatures $T_C=304.1$K, $T_C=647.1$ K and $T_C=970.0$ K and critical densities $\rho_C=467.6$ kg/m3, $\rho_C=322.0$ kg/m3 and $\rho_C=220.3$ kg/m3, respectively. It was proven that for the studied fluids the hypothesis of conformal invariance holds in temperature intervals determined from experimental data near their liquid-vapor critical points. The values of the temperature intervals in which the hypothesis of conformal invariance near the liquid-vapor critical points is fulfilled depend on the absolute values of the critical parameters of the studied fluids. Confirmation of the CI hypothesis also means that the temperature derivative of the coexistence-curve diameter retains the weak singularity with the exponent of the isochoric heat capacity [11-13]. 1. A.M. Polyakov, Conformal symmetry of critical fluctuations, JETP Lett. 12, 381–383 (1970). 2. A.A. Migdal, Conformal invariance and bootstrap, Phys. Lett. B 37(4), 386–388 (1971). doi: 10.1016/0370-2693(71)90211-5 3. A.V. Chalyi. What is Medicine? Basic Principles of Physics in Medicine and Beyond, Springer Nature Switzerland AG (2024). https//doi.org/10/1007/978-3031-64979-0 4. L.P. Kadanoff, Operator algebra and the determination of critical indices, Phys. Rev. Lett. 23(25), 1430–1433 (1969). 5. V.L. Pokrovskii, Feasibility of experimental verification of the conformal invariance hypothesis, JETP Lett. 17, 219–221 (1973). 6. A.Z. Patashinsky, V.L. Pokrovsky, Fluctuation Theory of Phase Transitions (Pergamon Press, Oxford, 1979). 7. R. Span, W. Wagner, Equations of state for technical applications. III. Results for polar fluids, Int. J. Thermophys. 24(1), 111–162(2003). doi: 10.1023/A:1022362231796 8. M.Z. Southard, D.W. Green, Perry’s Chemical Engineers’ Handbook, 9th ed. (McGraw-Hill Education, New York, 2019). 9. REFPROP Database, National Institute of Standards and Technology, SRD 23, Version 10 (2018). doi: 10.18434/T4/1502528 10. T.J. Bruno, T.J. Fortin, M.L. Huber, A. Laesecke, E.W. Lemmon, E. Mansfield, M.O. McLinden, S.L. Outcalt, R.A. Perkins, K.N.Urness, J.A. Widegren, Thermophysical Properties of Polyol Ester Lubricants, NISTIR 8263 (National Institute of Standards and Technology, 2019). doi: 10.6028/NIST.IR.8263 11. L.M. Artyukhovskaya, E.T. Shmanskaya, Yu.I. Shimanskii, Heptane coexistence curve near the critical point. JETP 63(3), 2153-2164, (1972). 12. L.A. Bulavin, Yu.I. Shimanskii. The singularity of the coexistence-curve diameter of ethane. JETP Lett 29(8) 482 (1979). 13. A.V. Chalyi, L.A. Bulavin, K.A. Chalyy. On the neutron optics of liquids, J/ Mol. Liquids 383, 121979 (2023).,

Liquid theory of spherical and unitary designs (STATISTICAL PHYSICS AND SOFT MATTER)

• Jorge Kurchan (Ècole Normale Supèrieure de Paris)

Room: Conference Hall "Designs" are sets of points, for example on a sphere, that have the property that averages of polynomials over the set coincide with averages over the whole sphere. Similarly for the unitary group. One can treat these points as interacting particles, and use liquid theory to study the problem. I will present the problem as seen from a physicist's point of view.

Staggering domino-like blast front motion in a one-dimensional cold gas (STATISTICAL PHYSICS AND SOFT MATTER)

• Yurij Holovatch (Yukhnovskii ICMP, NAS of Ukraine, Lviv)

Room: Conference Hall The relationship between the macroscopic dynamics of matter, viewed as a continuous medium, and that of its microscopic corpuscular constituents is a paramount challenge in physics. Its prominent 20th-century formulation is Hilbert’s sixth problem, which specifically calls for 'developing mathematically the limiting processes... which lead from the atomistic view to the laws of motion of continua' [1]. This applies to the transport of energy in a cold gas following an explosion – an instant injection of energy at a certain point. In this talk, we show that a typical and relatively simple model of this phenomenon may exhibit surprisingly counterintuitive behavior. We study the model in which point particles with masses $m,\mu, m, \mu, \dots$, $(m \geq \mu)$ are distributed on the positive half-line $\mathbb{R}_{+}$. Their dynamics are initiated by giving a positive velocity to the leftmost particle; in its course, the particles undergo elastic collisions. For this model with $m/\mu=2$, it has previously been established that the dynamics that start from random initial positions are consistent with predictions based on Euler's hydrodynamic equation [2]. In particular, they have the following properties: (i) the position of the rightmost particle (shock front) evolves as $t^\delta$ with $\delta <1$; (ii) recoiled particles behind the front enter the negative half-axis, $x\leq 0$, and form a splatter; (iii) particles in the splatter move ballistically and eventually take over the total energy of the system. We present numerical and analytical results for the dynamics of this model with nonrandom (typically equidistant) initial positions and various values of $m/\mu$ [3,4]. For $m/\mu=2$ and equidistant initial positions, our results qualitatively agree with those just mentioned. At the same time, we found an infinite family of numbers $\{\mathcal{M}_k\}$ such that, for $m/\mu = \mathcal{M}_k$, the hydrodynamic behavior mentioned changes drastically to the following. At each moment, only a single triplet $m, \mu, m$ is in motion, whereas all other particles are at rest. In the moving triplet, two heavy particles move to the right, while the lighter particle oscillates between them, transferring energy and momentum to the right. As a result, the shock front moves ballistically with an average velocity equal to the initial one. We refer to this regime - where motion is transferred sequentially from one triplet to the next - as 'staggering domino-like behavior.' This observation points to a breakdown of hydrodynamics and indicates non-ergodicity, as the system retains a dependence on the initial state at all times. We support our explicit calculations with molecular dynamics simulations. Such a staggering domino-like picture is obtained as an exact solution, which yields, in particular, explicit formulas for $\mathcal{M}_k$ and the particle velocities and positions. Its details and importance in a wider context are also discussed. [1]. A.N. Gorban. Phil. Trans. R. Soc. A 376 (2118) 2017023. [2]. S. Chakraborti, A. Dhar, P. L. Krapivsky, SciPost Phys. 13 (2022) 074. [3]. T. Holovatch, Yu. Kozitsky, K. Pilorz, Yu. Holovatch. Phys. Rev. E 112 (2025) L052101. [4]. T. Holovatch, Yu. Kozitsky, K. Pilorz, Yu. Holovatch. Phys. Rev. E, submitted, (2026), arXiv:2605.16125.

Entanglement in parameterized quantum circuits and its quantification on quantum computers (MATHEMATICAL PHYSICS)

• Khrystyna Gnatenko (Ivan Franko National University of Lviv)

Room: Conference Hall Entanglement in parameterized quantum circuits and its quantification on quantum computers Kh. P. Gnatenko Ivan Franko National University of Lviv, Professor Ivan Vakarchuk Department for Theoretical Physics, 12 Drahomanov St., Lviv, 79005 SoftServe Inc., 2d Sadova St., 79021 Lviv, Ukraine We study entanglement in multi-qubit variational quantum circuits with different structures of entangling blocks. For two- and multi-qubit variational states generated by circuits with $RY$ gates and entangling $CZ$ operators, we derive analytical expressions and recurrence relations for quantum correlators and the entanglement distance [1]. For a closed one-dimensional chain of n qubits, an explicit analytical expression for the entanglement of a qubit with the rest of the system for a two-layer variational protocol is obtained. It is shown that the entanglement of a given qubit is determined not only by its local gate parameters but also by the parameters of the gates acting on its nearest and next-nearest neighbors [1]. We also consider multi-qubit variational states represented by vertex- and edge-weighted graphs and constructed using single-layer circuits with $RX$ rotations and $RZZ$ gates. For quantum graph states of arbitrary structure, we derive the geometric measure of entanglement and quantum correlators and establish their relation to the edge- and vertex-weight structure in the neighborhoods of the corresponding graph vertices [2]. We show that the entanglement of a qubit in quantum graph states is determined by the weights of the incoming and outgoing edges associated with the corresponding vertex, as well as by its indegree and outdegree [3]. The analytical results are validated using quantum computing on the IBM Marrakesh and IBM Kingston quantum processors and the Qiskit AerSimulator, including noisy simulations [1-3]. The corresponding quantum circuits are implemented to investigate the dependence of the entanglement measures on circuit parameters and graph structure. The results of quantum computing are in a good agreement with the analytical results.. It is worth noting that the obtained dependencies of entanglement in variational quantum states on the parameters of variational quantum circuits and the structure of their entangling blocks are of fundamental importance. At the same time, they are relevant to potential applications in quantum computing. Variational quantum states and quantum graph states underly in a wide range of quantum algorithms, including quantum machine learning, variational quantum protocols, and quantum error correction. The analytical characterization of their entanglement, together with quantum protocols for its quantification using quantum computing, can therefore contribute to the design and improvement of quantum algorithms and to the identification of circuit architectures capable of generating and controlling a desired degree of entanglement. Also, the obtained relations between entanglement of quantum graph states and structural properties of graphs, vertex and edge weights, open up the possibility of studying them using quantum computing. [1] Kh. P. Gnatenko, A. Kaczmarek Properties of multi-qubit variational quantum states representing weighted graphs and their computing with quantum programming, arXiv:2604.00958 (2026). [2] Kh. P. Gnatenko, R. O. Hredil, V. Y. Pinchuk, M. Z. Seniak, Y. T. Shevchuk Entanglement distance of two- and multi-qubit variational states and its quantification with quantum computing, arXiv:2605.00259 (2026). [3] Kh. P. Gnatenko Entanglement of multi-qubit states representing directed networks and its detection with quantum computing Phys. Lett. A 521, 129815 [5 p.] (2024).

Baryon fluctuation signatures of the onset of deconfinement (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Mark Gorenstein (Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine)

Room: Conference Hall We predict an anomalous collision-energy dependence of proton-number fluctuations as a consequence of the onset of deconfinement in heavy-ion collisions at the nucleon-pair centre-of-mass energy (8 − 12) GeV. The effect arises from the change of properties of the effective degrees of freedom during the transition from confined and deconfined matter. The proposed interpretation provides a unified explanation of the collision-energy dependence of proton fluctuations together with the previously observed anomalies in hadron production, and yields semi-quantitative predictions without introducing parameters adjusted to the fluctuation data.

Equation of State of Strongly Interacting Matter from Physics-Informed Neural Networks (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Musfer Adzhymambetov (Bogolyubov Institute for Theoretical Physics)

Room: Conference Hall Understanding the properties of strongly interacting matter is one of the central challenges in high-energy physics. In heavy-ion collisions, nuclei are smashed together at relativistic speeds to recreate extreme conditions of temperature and density, briefly producing a state of matter known as the quark-gluon plasma. This hot, dense matter behaves as a nearly perfect liquid — flowing with remarkably low viscosity — and is best described by relativistic hydrodynamics, whose key input is the equation of state encoding the system's thermodynamic properties. The underlying theory, quantum chromodynamics, cannot yet be solved from first principles across the full phase diagram. Lattice QCD is reliable only at low baryon chemical potential, while the hadron resonance gas model holds only at low particle densities. Between them lies a critical gap — one that coincides precisely with the region being probed by next-generation experiments such as RHIC BES, FAIR, and CBM. In this talk, I present a neural-network approach to bridging this gap. The network is trained to reproduce lattice QCD and hadron resonance gas thermodynamics in their regimes of validity, while extrapolating into the uncharted high-baryon-density region in a manner that remains thermodynamically consistent — enforced through convexity-preserving architecture and derivative constraints, in the spirit of physics-informed neural networks. The result is a four-dimensional equation of state, $P(T, μ_B, μ_Q, μ_S)$, spanning the full phase space relevant to heavy-ion collisions. I will conclude by showing how this equation of state is implemented within a full relativistic hydrodynamic simulation framework. This work was partially supported by the National Research Foundation of Ukraine (project № 2025.07/0050).

Particle multiplicity fluctuations of quantum origin and high-multiplicity pp collision events (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Sergiy Akkelin (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

Room: Conference Hall The multiplicity dependence of the two-particle Bose-Einstein momentum correlation radii in pp collisions at the LHC has been measured at a fixed energy of collisions. One notable feature of these measurements is that the effective system’s volume, when extracted from the correlation radius parameters, appears to scale nearly linearly with charged-particle multiplicity [1-3], except for low multiplicities where initial state effects dominate and, quite unexpectedly, except for very high multiplicities where, at variance with the expected behavior for emission from hydrodynamically expanding systems, one sees systematic deviations from such a scaling behavior. That is, the striking feature of the data is that the correlation radius parameters become approximately independent of the particle multiplicity in the limit of very high multiplicities [1,2]. The question naturally arises: How can this controversy with hydrodynamics be resolved? In Ref. [4], we argue that quantum-origin multiplicity fluctuations dominate the fluctuations in particle multiplicity in high-multiplicity pp collision events at a fixed LHC energy. The quantum-to-classical transition of multiplicity fluctuations happens when the interference term between the corresponding states becomes negligible. Until this happens, superposition cannot be interpreted as a classical ensemble of its component states. To connect quantum fluctuations of particle multiplicity to event-by-event multiplicity fluctuations, we introduce the statistical ensemble of the multiplicity fluctuations of particles after the system’s freeze-out. We utilize the maximum entropy prescription to determine a quantum state at kinetic freeze-out and derive expressions for multiplicity-selected particle momentum spectra and correlation functions by applying a fixed particle-number constraint to this state. Then, we study how multiplicity fluctuations at high multiplicities impact the multiplicity-selected particle momentum spectra and correlation functions. In particular, we find that the effective system’s volume should become approximately independent of the particle multiplicity in the limit of very high multiplicities in multiplicity-selected collision events. References [1] ATLAS Collaboration, Eur. Phys. J. C 75, 466 (2015), https://doi.org/10.1140/epjc/s10052-015-3644-x; 82, 608 (2022), https://doi.org/10.1140/epjc/s10052-022-10472-0 . [2] A. M. Sirunyan et al. (CMS Collaboration), Phys. Rev. C 97, 064912 (2018), https://doi.org/10.1103/PhysRevC.97.064912 ; J. High Energy Phys. 03 (2020) 014, https://doi.org/10.1007/JHEP03(2020)014 . [3] S. Acharya et al. (ALICE Collaboration), Phys. Rev. C 109, 024915 (2024), https://doi.org/10.1103/PhysRevC.109.024915 . [4] S.V. Akkelin, Phys. Rev. D 112, 116007 (2025), https://doi.org/10.1103/k7mv-57bt .

Macroscopic rotational constraints on the neutron-star radius (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Alexander Magner (IInstitute for Nuclear Research of the National Academy of Sciences)

Room: Conference Hall The macroscopic model for neutron stars (NSs) as a cold perfect fluid in equilibrium within the Tolman-Oppenhiemer-Volkoff (TOV) theory is extended to a small rotational angular momentum I around the symmetry axis. The deformed NS surface was taken into account in the leptodermic approximation $a/R<<1$, where $a$ is an inner crust thickness and $R$ is the NS radius. Using the linear perturbation approach, $I/M^2<<1$, where $M$ is the NS mass (c=G=1), and the outer-inner Schwarzschild solutions in the zero-order approximation, one obtains analytically the first-order GRT results for the off-diagonal metric element $g_{t\varphi}$. Within Kerr approach using the spherical Boyer-Lindquist outer ($r > R$) and Hogan inner ($r < R$) coordinates, the GRT equation for $g_{t\varphi}$ has been solved in a separable outer-inner form. The surface density-gradient terms are taken into account through the macroscopic energy density $E(\rho)$ for the equation of state (EoS) within the Extended Thomas-Fermi (ETF) approach adopted to a strong gravitational field. Using a macroscopic rotational self-consistent approach we show that the relativistic moment of inertia (MI) $\Theta$ has a pole structure as function of the NS radius $R$, $\Theta_{av}/(1-\Theta_{t\varphi})$, through the statistically averaged $\Theta_{av}$ and time-angle gravity correlation $\Theta_{t\varphi}$ contributions. The latter appears because the off-diagonal gravitational element $g_{t\varphi}$ is self-consistently related to the NS angular momentum $I$. The MI contributions $\Theta_{av}$ and $\Theta_{t\varphi}$ are the sums of the volume and surface components derived through the ETF energy density $E(\rho)$. As the MI is asymptotically divergent at a certain NS radius $R_{rot}$, one obtains the constraint, $R < R_{rot}$, which is additional to the well-known radius restrictions coming from the Schwarzschild gravity metric and TOV approach. We obtained $R_{rot}$ as function of the radius $R$ in terms of the Schwarzschild parameters. For several well-known NSs with the observed mass $M$ and radius $R$ for enough large rotation periods, larger or of the order of 5 ms, one finds a good condition $I/M^2<<1$ for applicability of the linear perturbation approach. We found also the essential dependence of the MI $\Theta$ and radius constraint $R_{rot}$ on the surface tension coefficient $\sigma$, leptodermic parameter $a/R$, gravitational-nuclear incompressibility $K$, and deformation parameters. As perspectives, we are planning to find the rotation corrections to the TOV equations over the angular momentum parameter $I/M^2$ up to second order.

Strong interactions from scattering to matter: $^4$He atoms and nucleons (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Ubirajara van Kolck (European Center for Theoretical Studies in Nuclear Physics and Related Areas)

Room: Conference Hall Effective field theories (EFTs) allow for a systematic description of processes at a particular energy scale, even for strongly interacting systems where no small coupling constants exist. EFTs link scattering and matter, topics of a great tradition of research at BITP. I will discuss two contemporary systems where structure emerges from essentially one parameter: $^4$He atoms and nucleons.

The quest for the Hoyle-analog states in light hypernuclei (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Victor Vasilevsky (Bogolyubov Institute for Theoretical Physics)

Room: Conference Hall To resolve a long-standing problem of nuclear astrophysics regarding of synthesis of $^{12}$C and heavier nuclei, in 1953, F. Hoyle suggested that the nuclei $^{12}$C were created in a collision of three alpha particles. This collision leads to the creation of a very narrow (long-lived) 0$^{+}$ resonance state, which emits a photon and then transforms into a bound state of $^{12}$C. Moreover, F. Hoyle predicted the energy and width of the 0$^{+}$ resonance state with high precision. Later, this assumption was experimentally confirmed and now this resonance state is called the Hoyle state. Many theoretical models have been used to describe such an exotic state and to reveal its nature. A microscopic three-cluster method, proposed in [1], has been successfully applied in [2] to study the peculiarities of the Hoyle state and find the Hoyle-analog states [3] in a set of light nuclei. In the present work, we study the resonance structure of light hypernuclei $_{\Lambda}^{6}$H, $_{\Lambda}^{6}$He, $_{\Lambda}^{6}$Li, $_{\Lambda}^{7}$He, $_{\Lambda}^{7}$Li, $_{\Lambda}^{7}$Be, and try to find the Hoyle-analog states, i.e., the long-lived resonance states which can be formed in a three-cluster collision. The quest is performed with a three-cluster microscopic model, which was suggested in Ref. [1] and modified to study hypernuclei. The selected hypernuclei are considered as three-cluster systems, where one cluster is the lambda hyperon. For each hypernuclei we selected a three-cluster configuration, which has the minimal threshold energy among other three-cluster configurations. This dominant three-cluster configuration allows us to study bound states of a compound hypernuclear system and its resonance states in two- and three-cluster continua. In hypernuclei $\ _{\Lambda}^{6}$H, $_{\Lambda}^{6}$He, $_{\Lambda}^{6}$Li, $_{\Lambda}^{7}$He, $_{\Lambda}^{7}$Li, we found several very narrow resonance states, their total width is very small, less than 10 keV, and they lie close to the corresponding three-cluster threshold. The narrowest resonance states have wave-function structures typical of those of the Hoyle-analog states in ordinary nuclei [3]. Thus, the Hoyle analog states can be excited in hypernuclei $_{\Lambda}^{6}$H, $_{\Lambda}^{6}$He, $_{\Lambda}^{6}$Li, $_{\Lambda}^{7}$He, $_{\Lambda}^{7}$Li in triple collisions of three clusters, one of which is the lambda hyperon. We assume that the narrowest resonance states revealed by our model can be experimentally detected. [1]. V. S. Vasilevsky, A. V. Nesterov, F. Arickx, J. Broeckhove, “Algebraic model for scattering in three-s-cluster systems. I. Theoretical background”, Phys. Rev. C, vol. 63, 034606, 2001. [2]. V. S. Vasilevsky, F. Arickx, W. Vanroose, J. Broeckhove, “Microscopic cluster description of $^{12}$C”, Phys. Rev. C, vol. 85, 034318, 2012. [3]. V. S. Vasilevsky, K. Katō, N. Takibayev, “Systematic investigation of the Hoyle -analog states in light nuclei “, Phys. Rev. C, vol. 98, 024325, 2018.

Non-identical particle femtoscopy as a probe of the heavy-ion collision dynamics (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Volodymyr Shapoval (Bogolyubov Institute for Theoretical Physics)

Room: Conference Hall The momentum correlations in pairs of non-identical particles produced in heavy-ion collisions can be used to determine the space-time asymmetries in the radiation of the two particle species [1]. And these asymmetries, in turn, reflect the peculiarities of the underlying collision dynamics. Since the system created in a relativistic heavy-ion collision undergoes collective expansion, one of the explanations for the difference in average position and time of emission for different hadron species could be the different shift by the transverse collective flow. The other possible reasons include the different particle interaction cross sections, production via long-lived resonance decays, re-scattering at the hadronic stage of the collision, etc. [2]. However, in the experiment one can hardly separate one factor from another to trace their respective roles in gaining the observed result. That is why to analyze the situation in detail one should rather consider the simulation of the collision in realistic models, where one can fully control the process. In this work, we analyzed correlations in pion-kaon pairs based on the simulations of lead-lead collisions at the Large Hadron Collider in the well-known iHKM [3] and LQTH [4] models. The results were compared to the experimental data from the ALICE Collaboration [2]. The analysis was carried out at different average pair transverse velocities. The sizes of the particle emission sources and the displacements between the pion and kaon source centers were determined. It was found that the crucial factor affecting the emission asymmetry between pions and kaons are hadronic re-scatterings at the late ``afterburner'' stage of the system's evolution. The presence of a hadron cascade stage simulation in the iHKM model allows it to provide a much better description of the data as compared to the LQTH model, which lacks the corresponding stage. [1] R. Lednicky, V. L. Lyuboshits, B. Erazmus, D. Nouais, Phys. Lett. B **373**, 30 (1996); A. Kisiel, Phys. Rev. C **81**, 064906 (2010). [2] S. Acharya, *et al.* (ALICE collaboration), Phys. Lett. B **813**, 136030 (2021). [3] V. Yu. Naboka, Iu. A. Karpenko, Yu. M. Sinyukov, Phys. Rev. C **93**, 024902 (2016). [4] P. Bozek and I. Wyskiel-Piekarska, Phys. Rev. C **85**, 064915 (2012).

The mobility of a mono-vacancy in 2D graphene studied with molecular dynamics (CONDENSED MATTER PHYSICS)

• Ari Paavo Seitsonen (Département de Chimie, École Normale Supérieure)

Room: Conference Hall The graphene has become a widely investigated material since its controlled isolation and identification 20 years ago, and it started the boom of the two dimensional materials. The electronic, mechanical and other properties of graphene are affected by the native defects in it. Here we study the simple one, a mono-vacancy. A question about its mobility has been raised by the community of experimental groups performing imaging of graphene witht the Scanning Tunnelling Electron Microscopy (STEM), because they see In order to give an answer to this question we performed molecular dynamics simulations of the graphene with a mono-vacancy at different temperatures, and from the rate of diffusion we estimate the hopping rate of the vacancy and thus the time of temporary stability at a given site. The potential we used is a machine learning interaction potential fitted to data from similar simulations with the density functional theory. The fitted potential allows us to run much longer simulations at a modest computing cost, with a system that is also larger than feasible with electronic structure calculations. In this preliminary report of our results we compare our results with the earlier ones given in the literature. <img src="https://indico.bitp.kiev.ua/event/18/contributions/551/attachments/161/274/vmdscene-spin_density-v01.png" width="150" height="100"> The spin electron density on the atoms around the vacancy in graphene from the DFT

M.M. Bogolyubov and theoretical physics in Kharkiv (STATISTICAL PHYSICS AND SOFT MATTER)

• Yuriy Slyusarenko (O.I. Akhiezer Institute for Theoretical Physics, NSC KIPT and V.N. Karazin Kharkiv National University)

Room: Conference Hall The "genealogy" of theoretical physics in Kharkiv from the beginning of the 1930s to the present is presented. The connection is traced both at the level of research topics and at the level of interpersonal relations between representatives of the Kyiv school of theoretical physics, founded by M.M. Bogolyubov, and the Kharkiv school of theoretical physics, founded by L.D. Landau and O.I. Akhiezer. The main attention is paid to the intersection of research topics in statistical physics of both schools, in particular, to the methods of statistical physics in the theory of irreversible processes.

Cosmology Probes for Fundamental Physics (ASTROPHYSICS AND COSMOLOGY)

• Carlo Baccigalupi (International School for Advanced Studies)

Room: Conference Hall We briefly describe the relevance of combining the datasets from operating and future CMB and LSS probes for addressing the physics of the Early Universe, the Dark Cosmological Components as well as the latest results on Standard Model of Particle Physics, in the Neutrino Sector. We review methodologies, probes, as well as the recent results, in terms of cross-correlation and combination, and the future challenges towards the next decade, focusing on the joint efforts and collaborations involving excellence centers in Ukraine.

Ensemble-Averaged Axion–Photon Conversion in Turbulent Galaxy Clusters (ASTROPHYSICS AND COSMOLOGY)

• Oleksandr Khasai (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

Room: Conference Hall Axion-like particles (ALPs) coupled to photons can modify electromagnetic spectra through conversion in astrophysical magnetic fields. In galaxy clusters, turbulence makes this effect stochastic and strongly dependent on the magnetic-field realisation for individual sightlines. Recent work showed that averaging over ensembles of background active galactic nuclei transforms these fluctuations into a smooth, universal absorption-like feature, enhancing the sensitivity of cluster ALP searches [1,2]. We develop an analytic description of this ensemble-averaged signal and establish the connection between physical turbulence spectra and the domain models commonly used in numerical simulations. Turbulent fields are often represented by uniform domains with sizes distributed as $p(\Delta)\propto\Delta^{\beta-1}$, while a physical turbulent field is characterised by $\langle|B_k|^2\rangle\propto k^{-a-2}$, corresponding to an energy spectrum $\propto k^{-a}$ and $a=5/3$ for Kolmogorov turbulence. In the perturbative regime, the ensemble-averaged conversion probability is determined by the one-dimensional power spectrum of the transverse field along the line of sight [3]. Matching the exact domain-model correlator to the turbulent structure function gives $\beta = a - 2$ for $1 < a < 2$. Consequently, Kolmogorov turbulence corresponds to $\beta = -1/3$, i.e. $p(\Delta) \propto \Delta^{-4/3}$, rather than $\beta = 2/3$ as used in [4]. We also show that $\beta > 0$ universally produces an effective $k^{-2}$ spectrum because of the discontinuities at domain boundaries, while spectra with $a > 2$ cannot be reproduced by this class of models. Using this correspondence, we derive the ensemble-averaged conversion probability in closed form for arbitrary $\Delta_{\min}/\Delta_{\max}$ and obtain a simple two-power-law approximation. The resulting feature starts at $\omega_c\sim m_a^2\Delta_{\max}/2$, rises approximately as $\omega^a$, and saturates at high energies with an amplitude controlled by the magnetic-field correlation length. Thus, the inertial-range turbulence fixes the spectral shape, while the high-energy plateau retains an $\mathcal{O}(1)$ sensitivity to the modelling of the largest field scales. Our results provide an analytic dictionary between turbulent spectra and domain-size prescriptions, removing an ad hoc parameter from cluster ALP simulations. They also provide an analytic alternative to Monte-Carlo averaging over magnetic-field realisations, offering a practical framework for interpreting existing ensemble searches and constructing efficient templates for future observations [1,2]. References: [1]D. Malyshev, L. Zadorozhna, Yu. Bidasyuk, A. Santangelo, and O. Ruchayskiy. Constraints on axion-like particles from active galactic nuclei seen through galaxy clusters. Nature Astronomy, 9:1387–1395, September 2025. doi:10.1038/s41550-025-02621-8 [2]D. Malyshev, L. Zadorozhna, Yu. Bidasyuk, A. Santangelo, and O. Ruchayskiy. AGN spectral variability across activity states and searches for axion-like particles. arXiv e-prints, art. arXiv:2509.22344, September 2025. doi:10.48550/arXiv.2509.22344. [3]M. C. D. Marsh, J. H. Matthews, C. Reynolds, and P. Carenza. Fourier formalism for relativistic axion-photon conversion with astrophysical applications. Phys. Rev. D, 105(1):016013, 2022. doi:10.1103/PhysRevD.105.016013 [4]J. P. Conlon, F. Day, N. Jennings, S. Krippendorf, and M. Rummel. Constraints on Axion-Like Particles from Non-Observation of Spectral Modulations for X-ray Point Sources. JCAP, 07:005, 2017. doi:10.1088/1475-7516/2017/07/005.

Coherent effects in atomic K-shell ionization and characteristic X-ray emission by ultrashort high-energy electron bunches (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Vsevolod Skorobohatov

Room: Conference Hall The coherent effects present in atomic K-shell ionization and the subsequent emission of characteristic X-ray radiation (CXR) induced by ultrashort relativistic electron bunches are investigated [1]. The approach distinguishing close and distant collisions was applied to calculate the K-shell ionization cross section. The cross section associated with close collisions is independent on the number of electrons in the bunch and can be calculated using the approximation of hard binary electron-electron collisions. Meanwhile, the cross section associated with distant collisions is affected by coherent effects and was of primary interest. It was calculated based on the Weizsäcker-Williams method of equivalent photons. It was shown that the interference between the proper electromagnetic fields of single electrons can lead to a significant coherent enhancement of the ionization cross section in thin light-element targets, particularly beryllium and carbon. In particular, the case of a microbunched beam was investigated using a periodically modulated distribution of the bunch number of particles in longitudinal direction. According to calculations made for parameters of bunches achievable at modern X-ray free electron lasers, a strong resonant amplification of the cross section occurs. This leads to an enhancement of the ionization cross section by several orders of magnitude for a wide range of microbunching periods. Moreover, the analysis was extended to targets of arbitrary thickness to study the evolution of the K-shell ionization cross section caused by the medium polarization (density effect) along the beam propagation path. It was found that the cross section decreases with increasing the depth of the beam penetration into the target, reaching a plateau when the penetration depth significantly exceeds the absorption length of a photon with an energy equal to the K-shell ionization threshold. Furthermore, it was shown that the main contribution to the CXR photons emitted from the target comes from a thin near-surface layer, whose thickness can be much smaller than the CXR attenuation length, unlike in the case of a single electron interacting with the target. The reasons for this are discussed. The obtained results and the considered coherent effects could be applied to the development of new techniques for diagnostics of parameters of subfemtosecond electron bunches.

Seeing Effective Field Theory of Neutron Decay through of Double Categories (MATHEMATICAL PHYSICS)

• Stepan Moskaliuk (Bogoliubov Institute for Theoretical Physics)

Room: Conference Hall In this talk the Standard Model of the neutron decay is described by the exchange of the electroweak $W$ boson. However, energy scales for this process ($\sim \mathrm{MeV}$) are well below the electroweak scale ($\sim 100~\mathrm{GeV}$). Consequently, the historical description within the low-energy effective field theory (EFT) is the correct physics picture for the neutron decay, on the one hand. On the other hand, expansion of the categorical point of view on many areas of mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new additional structures on categories. One of such structures, a double category, is considered in this talk. The double category structure is defined as generalization of the bicategory structure. The use of EFT techniques and category-theoretical methods is not a mere reformulation of the problem. Different formulations of EFTs lead to identical mappings of one set of finite quantities (parameters of the theory) to another set of finite quantities (results of measurements, cross-sections, etc.). It means that the presence of infinities (quartic, quadratic and etc.) is formalism dependent, and thus their absence or presence should not be served as an argument for selecting this or that physical theory. This shows that the so-called technical hierarchy problem (the sensitivity of low-energy physics to high-energy physics) depends on the formulation of quantum field theory, and, therefore, is devoid of physical meaning, at least for renormalisable theories. The EFT also provides a rigorous way to connect scales and estimate uncertainties. Moreover, EFT methods can bring new insights to the problem. In fact, by providing a simple framework to analyze hadronic correlation functions, the study of neutron decay to $\mathcal{O} (G_F \alpha)$ in Heavy Baryon Chiral Perturbation Theory (HBChPT) has uncovered a new \%-level ``inner" correction to the ratio $g_A/g_V$ of axial-vector to vector nucleon couplings, missed in previous analyses based on current algebra. The leading-order amplitude for the neutron decay is proportional to the Fermi coupling constant $\mathrm{G}_\mathrm{F}$, which is precisely determined from the muon decay. Charged currents with quarks introduce the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $V_{ud}$ to the neutron beta decay amplitude. At low energies, the neutron decay is described by two coupling constants: the vector $g_\mathrm{V}$ and the axial-vector $g_\mathrm{A}$. In the reference of this talk, there are presented all theoretical works rely on the precise evaluation of electroweak, quantum chromodynamics (QCD), and long-distance hadronic contributions to these coupling constants. In the HBChPT framework for single-nucleon weak charged-current (CC) processes, the active degrees of freedom are the light leptons, photons, pions, and nucleons. The effect of both electroweak- and other hadronic-scale physics is encoded in a number of low-energy constants (LECs). The goal of this talk is to develop a matching procedure to express the relevant LECs in terms of perturbatively calculable Wilson coefficients and hadronic correlation functions that can then be estimated with non-perturbative methods, such as dispersive methods or lattice QCD. Since there are multiple thresholds, the electroweak scale $\sim M_{W,Z}$, the chiral symmetry breaking scale $\Lambda_\chi \sim m_N\sim$~GeV, with $m_N$ the mass of nucleon, and the pion mass, we adopt a multi-step matching strategy. The first step connects the Standard Model EFT to the low-energy effective theory (LEFT) below the weak scale, which coincides with the $V-A$ theory of weak interactions augmented by QED and QCD. This is a perturbative matching step. The second step connects the double category of LEFT to the double category of HBChPT by double category functors and involves non-perturbative physics. The third step consists of integrating out the pions, by matching the double category of HBChPT onto a double category of pionless EFT.

Resetting search for multiple targets (STATISTICAL PHYSICS AND SOFT MATTER)

• Leonid Christophorov (Bogolyubov Institute for Theoretical Physics, NAS Ukraine)

Room: Conference Hall Research into stochastic processes with resetting is currently in a phase of intensive development. After the initial period, when the main effects of optimizing target search in basic random walk models were identified, researchers moved on to studying more complex problems with a focus on their practical aspects. One example is the process of sequentially locating/destroying multiple targets by a random walker, as a prototype of the DNA repair process. In this report, we show that such a process can be fully described in terms of the theory of random walks with resetting along a one-dimensional lattice with a single target that we developed earlier [1]. For the case of clusters of targets located at lattice nodes, exact analytical expressions for the mean times Тm of the consecutive annihilation of all *m* targets, as well as a recursive relationship, are found. Calculations show that in certain topologies of the model, the counter-intuitive effect of accelerated annihilation with increasing *m*, Т*m* < Т*m*-1 (or with increasing the distance between targets), is maintained for *m* > 1 in both infinite and finite chains. In the latter, the effect is present even in the absence of resetting. We analyse in detail the nature of this effect and show that it is not generated by Poissonian resetting, which rather weakens the effect, but by the statistical properties of random walks [2]. The work is performed within the Project 0121U109816 of the NAS of Ukraine. Partial support from the Simons Foundation is gratefully acknowledged. 1. L.N. Christophorov. J. Phys. A: Math. Theor. 54, 015001 (2021); J. Phys. A: Math. Theor. 55, 155006 (2022); Ukr. J. Phys. 69, 591 (2024). 2. L.N. Christophorov. J. Phys. A: Math. Theor. 59, 015002 (2026).

Magnons as uncharged carriers for quantum communication between nanomagnets (QUANTUM MATERIALS)

• Serhii Tunyk (Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine)

Room: Conference Hall Recent experimental studies have shown that magnonics—an independent branch of spintronics—can realize its potential in nanotechnology applications involving magnetophotonics, thermal nanoconversion, magnonic capacitors, magnonic transistors, and other fields. Magnons are very good candidates for use in quantum communication. This is because the transport of magnons as uncharged quasiparticles can occur without the generation of Joule heat, and, just as with charged carriers, this transport can be controlled using magnetic and electric fields. We propose a physical mechanism whereby a localized spin excitation (Kittel magnon) generated in one microwave cavity can be resonantly transferred to another cavity via a ferromagnetic chain connecting the nanomagnets embedded in the cavities. It is shown that long-range magnon transfer can be achieved via coherent one-step tunneling of magnons between nanomagnets. Our theoretical study is based on a model in which, for fixed nanomagnet spin values, the states are determined by macrospin projections, and the ferromagnetic chain acts as a mediating scattering center. The coupling between spin excitations in the "nanomagnet A - ferromagnetic chain - nanomagnet B" hybrid structure (AFB structure) is mediated by the Heisenberg exchange interaction between the spins of adjacent paramagnetic units of the structure. Based on this model, analytical formulas were derived that made it possible to understand the physics of controlling magnon flow using magnetic fields; these fields tune the Kittel magnon frequency to the frequencies of delocalized magnons in the AFB structure. The main results of the study include the following. Analytical expressions for the magnon transport rate and magnon flow are obtained and key parameters controlling off-resonant and resonant magnon tunneling regimes are indicated. Physical conditions are determined under which peak values of the rate characterizing the process of resonant transmission of the Kittel magnon arise both at a fixed tunneling energy with an arbitrary number of units in the ferromagnetic chain or at a fixed number of chain units with a changing tunneling energy. A mechanism of coherent transfer is proposed, based on the premise that the spin states of a bridge, containing magnetically ordered paramagnetic units, play a virtual role. This facilitates a specific quantum exchange of magnons both within the bridge and between its terminal units and the adjacent nanomagnets. As a result, a long-range superexchange coupling arises between magnetostatic spin excitations, which ensures a tunnel regime of magnon transport between nanomagnets. It was also shown that due to the strong photon-magnon coupling in the microwave cavity, at a certain magnetic field, the tunneling flow of magnons can reach an additional peak value, which reflects the process of resonant photon-to-magnon conversion [1]. The obtained results indicate the potential for using magnons for quantum communication in hybrid structures where the transduction of one type of quasiparticle into another (in our case, photons and magnons) is possible. This work is partialy supported by the project of the Ministry of Education and Science of Ukraine «Development of theoretical and computational methods for the study of micro- and macrosystems in quantum technology” [1] E. G. Petrov, S. M. Tunyk, V.V. Gorbach, Phys. Rev. Appl., 25, 024072 (2026).

Physical modeling of macroscopic properties of the complex many-particle, poly-dispersive micromechanical (granular) systems (STATISTICAL PHYSICS AND SOFT MATTER)

• Oleg Gerasymov (Odesa National University)

Room: Conference Hall Physical modeling of macroscopic properties of the complex many-particle, poly-dispersive micromechanical (granular) systems O.I. Gerasymov*, A.Ya. Spivak# *State University of Intelligent Technology and Telecommunications, Odesa *National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute, Kyiv Odesa National Mechnikov’s University The study of the influence on the formation of macroscopic properties of multi-component mixtures is a complex and continuing to be an urgent task of fundamental physics and its numerous applications [1]. The traditional difficulties in determining reference states are supplemented by the difficulties of taking into account the effect of compaction in multicomponent mixtures. The task of describing the relationships between the micro- and macro-parameters of such systems is further complicated by the fact that multi-component mixtures (even if they are granular) can be in various states of aggregation from gaseous and liquid to crystalline. Presented paper develops theoretical approaches to the description of macroscopic (compressibility) and structural (compaction) characteristics of complex many-particle, poly-dispersive multi-component mixtures, using Kirkwood-Buff's semi-phenomenological algorithm [2], molecular models like Carnahan-Starling-Mansoori [3]. Based on a comparative analysis would be build a prognostic base for the practical application of the results obtained in order to optimize (achieve the required values) of control parameters in liquid, granular mixtures by manipulation of their composition and/or compaction. Along this line, using the Carnahan–Starling–Mansoori hard-sphere conglomeration models and the Kirkwood–Buff statistical theory, the effect of compaction (packing) on the compressibility of a binary granular mixture has been analyzed [4]. The theoretical results are compared with the experimental ones obtained in alternative studies of the systems whose internal structure corresponds to the construction characteristics of the model [5]. The possibility of the maximum packing effect at special dispersion and mole fraction values of the components has been shown. The existence of the limit and intermediate states of the mixture with a predominant concentration of one of the components and the possibility of the most adequate description of the system properties in such states using one of the above-mentioned approaches have been demonstrated. The interval of values for the component volume fractions has been determined, where both approaches well describe the data of corresponding experiments. References [1] O.I. Gerasymov. Physics of granular materials. Odesa, TES, 2015. 264p. [2] J.G. Kirkwood, F.P. Buff. The statistical mechanical theory of solutions. I. J. Chem. Phys. 19, 774. [3] G.A. Mansoori, N.F. Carnahan, K.E. Starling, T.W. Leland, Jr. Equilibrium thermodynamic properties of the mixture of hard spheres. J. Chem. Phys. 54, 1523 (1971). [4] O.I. Gerasymov, A.Ya. Spivak. Packing and compressibility of binary micromechanical (granular) systems. Ukr. J. Phys. 70, No. 8, 543 (2025). [5] S. Pillitteri, G. Lumay, E. Opsomer, N. Vandewalle. How size ratio and segregation affect the packing of binary granular mixtures. Soft Matt. 16, 9094 (2020).

Modern trends in plasma wakefield acceleration (HIGH ENERGY PHYSICS AND NUCLEAR MATTER)

• Vasyl Maslov

Room: Conference Hall High-efficiency acceleration of charged particle beams in the plasma wakefield accelerator was studied experimentally and by numerical simulation. The most impressive experimental results [1] until now in electron accelerating by a wakefield, excited in a plasma, have been achieved using capillary-generated plasma. Plasma-wakefield acceleration provides high accelerating gradients [1,2], promises compact accelerators of high-brightness and high-energy electron beams. Applications of plasma-wakefield accelerators, in particular, particle colliders and free-electron lasers demand low energy spread beams, their small emittance, high current of accelerated bunches, large transformer ratio and high-efficiency operation. Achievement of these requires plateau formation on both the accelerating field for witness-bunch and the decelerating fields for driver-bunch. As it is known plateau formation is possible by controlled beam loading with careful shaping current profile and beam charge selection. We will demonstrate by numerical simulation by PIC code and analytically such optimal beam loading in plasma wakefield accelerators. Problems of acceleration of positron bunches in plasma, focusing and stable transport of electron and positron bunches in plasma are important. In the blowout regime the hose instability can appear. Earlier investigations [3,4] show that the instability is essentially suppressed if the focusing force is inhomogeneous along the bubble, and radial inhomogeneity can be additional effect. The problem of the instability can be solved in weakly nonlinear regime. In weakly nonlinear regime throughout the areas of the driver and witness bunches the focusing force is inhomogeneous. Radial inhomogeneity of residual plasma electron distribution also leads to bunch stabilization. We will present results of analytical investigation of hose instability suppression in plasma wakefield accelerator driven by electron bunch in the weakly nonlinear and blowout regimes. The resonant sequence of electron bunches can be unstable due to the destruction of the bunches. In this report we show by numerical simulation and analytically the possible way of suppressing this instability by shaping of the bunches. We will present in the paper results on: - wakefield passive plasma lenses (due to loading effect) for identical focusing of short or long homogeneous electron or positron bunch or Gaussian bunch depending on its length, charge for stable electron or positron beam propagation in a plasma column; - optimal beam loading for the self-consistent distributions of a decelerating wakefield of plateau type for a driver-bunch and an accelerating wakefield of plateau type for a witness-bunch during all time of acceleration; - control of optimal field shape (by loading effect), accelerating electron or positron bunch in plasma wakefield; - obtaining long electron witness-bunch of good quality (due to loading effect) in plasma wakefield accelerator at high transformer ratio, - damping hose instability in plasma wakefield accelerator; - double bunches and twin-bunch in conditions and places of best bunch stability with plateaus on wakefield in PWFA. References 1.W.P. Leemans et al. Phys. Rev. Lett. 113 (2014) 245002. 2.V.I.Maslov et al. Problems of Atomic Science and Technology. 6, 52 (2021). 3.A.Martinez de la Ossa et al. Phys. Rev. Let. 121, 064803 (2018). 4.G.Loisch et al. J.Phys.: Conf. Ser. 1596, 012003 (2020).

q and mu extensions of special function in quantum field theory (MATHEMATICAL PHYSICS)

• Johannes Bluemlein

Room: Conference Hall Analytic higher order perturbative calculations in quantum field theory lead to special function spaces representig the Feynman integrals. We report on the recently obtained $q$- and $\mu$-extensions of these special function spaces.

Propagation of correlations in quantum systems of many particles and kinetic equations (MATHEMATICAL PHYSICS)

• Viktor Gerasimenko (Institute of mathematics NAS of Ukraine)

Room: Conference Hall The talk provides an overview of recent progress in the mathematical understanding of kinetic equations that govern quantum systems with many particles. The talk will begin by discussing an approach to describing the evolution of correlations in systems of many quantum particles. This method is based on the von Neumann hierarchy of evolution equations for a sequence of correlation operators or cumulants of the density operators. It will be proved that the constructed dynamics of correlations underlie the description of the evolution of the state, both for finitely and infinitely many quantum particles, governed by the BBGKY hierarchy for reduced density operators or by the hierarchy of nonlinear evolution equations for reduced correlation operators. Furthermore, this discussion will demonstrate that the concept of cumulants of the groups of operators for the von Neumann equations underlies nonperturbative solutions to hierarchies of fundamental equations that describe the evolution of observables and of the state of many quantum particles, as well as forming a foundation for the kinetic description of their collective behavior. The talk will also introduce a new approach to the problem of a rigorous description of kinetic evolution using reduced observables. One of the advantages of the developed approach to deriving kinetic equations from the underlying dynamics of many particles is the ability to construct kinetic equations that incorporate initial correlations and to describe the processes of propagating these initial correlations under appropriate scaling approximations. References [1] Gerasimenko, V.I. Hierarchies of quantum evolution equations and dynamics of many-particle correlations, in: Statistical Mechanics and Random Walks: Principles, Processes and Applications, N.Y.: Nova Sci. Publ., Inc., 2013, 233-288. [2] Gerasimenko, V.I., Gapyak, I.V. Cumulant expansions of operator groups of quantum many-particle systems. Ukrainian Math. J. 78(3-4) 218-234 (2026). doi:10.3842/umzh.v78i3-4.9375 [3] Gerasimenko, V.I. The Heisenberg picture of quantum kinetic evolution in the mean-field limit. Kinetic & Related Models. 4(1) 385-399 (2011). doi:10.3934/krm.2011.4.385 [4] Gerasimenko V.I., Gapyak I.V. Propagation of correlations in a hard-sphere system. J Stat. Phys. 189(2), (2022). doi:10.1007/s10955-022-02958-8 [5] Gerasimenko, V.I., Gapyak, I.V. Boltzmann-Grad asymptotic behavior of collisional dynamics. Reviews in Math. Phys. 33 2130001 32 (2021). doi:10.1142/S0129055X21300016

The uses of the SO(5)/SO(2) Stiefel sigma model for the unified Zhang's model (MATHEMATICAL PHYSICS)

• Yuliia Lunha (Bogolubov Institute for Theoretical Physics)

Room: Conference Hall We investigate the critical behavior and phase structure of nonlinear sigma models on real Stiefel manifolds SO(N)/SO(N-k), with particular focus on the SO(5)/SO(2) model and its relation to the $SO(5)$-based Zhang model of competing antiferromagnetic and superconducting orders. The Stiefel model is characterized by two effective interaction coupling constants, which give rise to a tetracritical regime implying, in particular, the appearance of the phase with coexistence of antiferromagnetic and superconducting orders. We analyze the scaling behavior and properties of the four phases using both Hamiltonian and Lagrangian formulations. In particular, we determine quasiparticle masses and apply these to characterize the symmetry breaking in different phases, including the mixed phase where the two orders coexist. As one of our main results we present the determination of "transverse" critical exponents for the tetracritical point. These exponents complement the previously obtained critical exponents in the (T)-direction and provide a more complete characterization of the associated universality classes. Note that the transverse critical exponents are obtained for the general class of Stiefel models SO(N)/SO(N-k). We further examine the electron–hole asymmetry, which is not intrinsically incorporated in the Zhang model but emerges naturally in the Stiefel model framework. For the SO(5)/SO(2) model, the resulting carrier charge has the physically relevant sign, in contrast to the SO(5)/SO(3) Stiefel model which, in addition, does not exhibit tetracritical behavior. The obtained results establish an important connection between the critical structure (and phases) of Stiefel sigma models and the phenomenology of competing antiferromagnetic and superconducting orders.

The exact expression for increasing selectivity through statistical fluctuations in a system with a threshold (MATHEMATICAL PHYSICS)

• Oleksandr Vidybida (Bogolyubov Institute for Theoretical Physics)

Room: Conference Hall In various statistically defined situations, like referendum, epidemic threshold, mass service process or a chemical sensor the probability of overall output coincides with the probability that a threshold $N_0$ number of elementary events has been achieved. The latter depends on the probability $p$ that a single elementary event happens. Elementary event for a referendum case is the positive vote of a single voter; for a chemical sensor $-$ is the ligand binding by a single receptor in the sensor. The probability $p$ of elementary event may depend on some external factor $-$ campaigning type L for the referendum case, or the ligand type L applied in the case of chemical sensor. This constitutes the selectivity of elementary event. Naturally, the probability that the threshold $N_0$ is achieved depends on L as well. This constitutes the selectivity of essential event. Any of the two selectivities can be expressed by means of a dimensionless non-negative number. We derive a concise mathematical expression, for comparing the two selectivities, based on the incomplete beta-function, or on a continued fraction. Possible application in a chemical sensor is discussed.

Irregular conformal field theory and Painlevé equations (MATHEMATICAL PHYSICS)

• Nikolai Iorgov (Bogolyubov Institute for Theoretical Physics)

Room: Conference Hall In this talk, a notion of irregular conformal blocks in two-dimensional conformal field theory will be presented. It is expected that such irregular conformal blocks are related to the isomonodromic tau functions of Painlevé equations. I will consider, as an example, the Painlevé I equation and give details of the relation to irregular conformal field theory.

Long-time asymptotic series for the Painleve II equation: Riemann-Hilbert approach (MATHEMATICAL PHYSICS)

• Yurii Zhuravlov (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

Room: Conference Hall We elaborate a systematic way to obtain higher order contributions in the nonlinear steepest descent method for Riemann-Hilbert problem associated with homogeneous Painleve II equation. The problem is reformulated as a matrix factorization problem on two circles and can be solved perturbatively reducing it to finite systems of algebraic linear equations. The method is applied to find explicitly long-time asymptotic behaviour for tau function of Painleve II equation.

Canonization-based symmetry breaking in an integrable four-component nonlinear dynamical system on a quasi-one-dimensional lattice with background-controlled intersite coupling (MATHEMATICAL PHYSICS)

• Oleksiy O. Vakhnenko (Bogolyubov Institute for Theoretical Physics)

Room: Conference Hall Eleven years ago we developed the four-component nonlinear integrable dynamical system on a ribbon of two-leg triangular lattice with the common coherent and uncommon background-controlled intersite couplings [1, 2]. The system can be classified as a sort of semi-discrete nonlinear Schrödinger system. It characterized by four basic (independent) fields on zero background and two concomitant (dependent) fields on nonzero background. Due to nonzero background values of concomitant fields the entire Poisson structure of semi-discrete nonlinear system acquires essentially nonstandard form veiling the true physical interpretation of basic fields. Looking for a prospective physical applications of suggested semi-discrete nonlinear integrable system to the modeling of transport phenomena in long macromolecules or other quasi-one-dimensional physical objects, we suggested rather sophisticated multistage transformation to the semi-discrete nonlinear integrable system, characterized by the canonical Poisson structure and physically motivated field functions as well as by the standard canonical Hamiltonian formulation [3, 4, 5, 6]. As a result, we obtained two distinct but physically equivalent realizations of canonized semi-discrete four-component nonlinear integrable system, each one being manifested by a pronounced symmetry breaking between the so-called strong two-component and weak two-component subsystems. The rate of symmetry breaking is governed by the nonnegatively defined background parameter µν, so that for µν = 0 the symmetry between subsystems becomes totally restored. We believe, the value of background parameter µν could be regulated by external conditions imposed on a lattice. For undercritical values µν < 1 of background parameter µν each particular canonized system demonstrates bright excitation regime both in strong and weak subsystems, though the density of excitations in strong subsystem prevails over the density of excitations in weak subsystem. For overcritical values µν > 1 of background parameter µν each particular canonized system demonstrates bright excitation regime in strong subsystem and dark excitation regime in weak subsystem. The crossover between the bright–bright and bright–dark regimes of excitation dynamics established for the case of attractive nonlinearity occurs in the very critical point µν = 1. References [1] O.O. Vakhnenko. Integrable nonlinear Schr¨odinger system on a triangular-lattice ribbon, J. Phys. Soc. Japan 84(1), 014003 (12 pages) (2015). [2] O.O. Vakhnenko. Nonlinear integrable model of Frenkel-like excitations on a ribbon of triangular lattice, J. Math. Phys. 56(3), 033505 (21 pages) (2015). [3] O.O. Vakhnenko. Symmetry-broken canonizations of the semi-discrete integrable nonlinear Schr¨odinger system with background-controlled intersite coupling, J. Math. Phys. 57(11), 113504 (16 pages) (2016). [4] O.O. Vakhnenko. Semi-discrete integrable nonlinear Schr¨odinger system with background-controlled inter-site resonant coupling, J. Nonlin. Math. Phys. 24(2), 250–302 (2017). [5] O.O. Vakhnenko. Distinctive features of the integrable nonlinear Schr¨odinger system on a ribbon of triangular lattice, Ukr. J. Phys. 62(3), 271–282 (2017). [6] O.O. Vakhnenko, V.O. Vakhnenko, and A.P. Verchenko. Physical insight into the semi-discrete nonlinear integrable systems with the true and false multicomponentness, Chaos Solitons Fractals 200(2), 117043 (24 pages) (2025).

Resonant tunneling through one-point singular potentials (MATHEMATICAL PHYSICS)

• Alexander Zolotaryuk

Room: Conference Hall In one-dimensional quantum mechanics, shrinking a system to isolated points (set of Lebesgue's measure zero) leads to exactly solvable models. These models are referred to as point (contact or zero-range) interactions (PIs). In these cases,resolvents and spectra of Schroedinger operators, scattering coefficients and other characteristics can analytically be computed. Currently, because of the rapid progress in fabricating nanoscale quantum devices, of particular importance is the point modeling of different structures like quantum waveguides, spectral filters, or infinitesimally thin sheets. We have initiated a new project in the domain of PIs regarding a resonant tunneling through zero-range potentials being more singular than a traditional Dirac's delta potential. A typical example is the distributional potential in the form of a spatial derivative of the delta function. Using here a very simple two-scale (two-parameter) regularization scheme, we observe that different pathways $\Delta'_{\varepsilon}(x) \to \delta'(x)$ as $\varepsilon \to 0$ realize different PIs with the following three types of boundary conditions on the wave function $\psi(x)$: i) $\psi(-0) =\psi(+0)=0$ (separated with full reflection); ii) $\psi(+0)=\theta_n \psi(-0),~~\psi'(+0) = \theta_n^{-1}\psi'(-0)$, $\theta_n \in R$, $n \in Z$ (non-separated with resonant tunneling); iii) $\psi(+0)=\theta_n \psi(-0),~~\psi'(+0) = \alpha_n \psi(-0) +\theta_n^{-1}\psi'(-0),$ $\alpha_n \in R $ (non-separated with resonant tunneling having a single bound state at each $n$). For each of these types, the regions on the plane of two squeezing parameters are indicated explicitly. Recent literature: 1. A.V. Zolotaryuk and Y. Zolotaryuk, ``Scattering data and bound states of a squeezed double-layer structure'', *J. Phys. A: Math. Theor.* **54** (2021) 035201; [doi.org/10.1088/1751-8121/abd156][1] 2. Y. Zolotaryuk and A.V. Zolotaryuk, ``Influence of a squeezed prewell on tunneling properties and bound states in heterostructures'', *Annals of Physics* **477** (2025) 169999; [doi.org/10.1016/j.aop.2025.169999][2] 3. Y. Zolotaryuk and A.V. Zolotaryuk, ``Conditions for perfect transmission of quantum particles across layered heterostructures and resonance effects of an auxiliary well potential'', *Front. Appl. Math. Stat.* **11** (2015) 1636414; [doi.org/10.3389/fams.2025.1636414][3] [1]: http://doi.org/10.1088/1751-8121/abd156 [2]: http://doi.org/10.1016/j.aop.2025.169999 [3]: http://doi.org/10.3389/fams.2025.1636414

Low-Rank Split-Operator Propagation for Structured Open Quantum Systems (MATHEMATICAL PHYSICS)

• Roman Ovsiannikov (NSC «Kharkov Institute of Physics and Technology»)

Room: Conference Hall Direct numerical simulation of open quantum systems is limited by the quadratic memory cost of storing the density matrix. We present a deterministic low-rank propagation method for time-local Markovian dynamics. The method applies to Hamiltonians composed of a time-dependent diagonal part and terms that become tridiagonal after suitable permutations of the basis, as well as to collapse operators with diagonal or narrow-banded representations. The density matrix is represented by a low-rank ensemble of state vectors. Coherent evolution is advanced using a symmetric Suzuki–Trotter decomposition: diagonal factors are applied exactly, while tridiagonal factors are evaluated using Cayley transforms that require only solving tridiagonal linear systems. Dissipation is incorporated through infinitesimal Kraus branches, after which the enlarged ensemble is compressed to a prescribed rank using a small Gram matrix. For a fixed retained rank and number of collapse channels, the memory requirement and the dominant computational operations scale linearly with the Hilbert-space dimension. The method is benchmarked on a driven finite-spin model of an NV-center ensemble coupled to a microwave cavity. The interaction terms become tridiagonal in different basis orderings, while the cavity and collective-spin collapse operators retain a banded structure. Comparison with full-density-matrix simulations in QuTiP shows close agreement for the cavity quadrature variance in the tested regime, while the integrated errors of the monitored observables decrease systematically as the retained rank is increased from 2 to 16. Pure-propagation timing benchmarks exhibit near-linear scaling, with fitted exponents between 1.09 and 1.23. The method is therefore most effective when the density matrix remains approximately low rank; strongly mixed states and continuously pumped lasing regimes may require larger ranks and reduce the computational advantage.

Generic regularity of the two-component Novikov equation (MATHEMATICAL PHYSICS)

• Yan Rybalko (B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine)

Room: Conference Hall This talk concerns the Cauchy problem for the following two-component Novikov system: $\begin{align} &m_t+(uvm)_x+u_xvm=0, && m=m(t,x),\,u=u(t,x),\,v=v(t,x),\\ &n_t+(uvn)_x+uv_xn=0, && n=n(t,x),\\ &m=u-u_{xx},\,\,n=v-v_{xx}, && u,v\in\mathbb{R},\quad t,x\in\mathbb{R}, \end{align}$ It is well-known that this system admits the wave-breaking phenomena: the slope of solution corresponding to the smooth initial data can blow-up in finite time. The goal is to establish the generic regularity for the two-component Novikov system. More in detail, we show that there exists an open dense subset of initial data, such that the corresponding global weak solutions (which exist beyond blow-up) retain certain regularity properties in the $t,x$ plane. Applying the Bressan and Chen's approach [1], originally developed for the nonlinear variational wave equation, we prove the following result [2]. **Theorem.** Consider the regular initial data $(u_0,v_0)$ in the metric space $\Upsilon^k\subset\left(C^k\right)^2\cap\left(H^1\right)^2$, $k\geq5$, see [2] for details. Then for any $T>0$ there exists an open in $\Upsilon^k$ and dense in $\Upsilon^{k-1}\cap C^k_{\mathrm{loc}}$ subset $\mathcal{M}_T\subset\Upsilon^k$, such that for any initial data $(u_0,v_0)\in\mathcal{M}_T$ the corresponding global weak solution $(u,v)(t)$ satisfies the following regularity properties. There exist two sets of piecewise $C^{k-1}$ curves, say $\left\{\mathbf{C}_i^W\right\}_{i=1}^{N_1}, \left\{\mathbf{C}_j^Z\right\}_{j=1}^{N_2}\subset[-T,T]\times\mathbb{R}$, such that - both components $u$ and $v$ are $C^k$ regular away from the characteristic sets $\mathbf{C}_i^W$ and $\mathbf{C}_j^Z$ - $u$ is of class $C^1$ along each $\mathbf{C}_j^Z$ and $v$ is of class $C^1$ along each $\mathbf{C}_i^W$. [1] A. Bressan, G. Chen. Generic regularity of conservative solutions to a nonlinear wave equation. Ann. I. H. Poincaré 34 (2017) 335--354. [2] K.H. Karlsen, Ya. Rybalko. Generic regularity and Lipschitz metric for a two-component Novikov system. arXiv :2512.13305v2 (2026).

Manifestation of bilinear flexo-antiferrodistortive coupling at twins and antiphase boundaries in ferroelastics (CONDENSED MATTER PHYSICS)

• Anna Morozovska (Інститут фізики НАН України)

Room: Conference Hall The flexoelectric-type coupling between the gradients of electric polarization, described by a true polar vector $\vec{P}$, and the antiphase rotation of structural groups, described by an axial pseudovector $\vec{\Phi }$, can lead to the appearance of interfacial polarization at the twin walls, antiphase boundaries and surfaces of antiferrodistortive (AFD) ferroelastics [1]. The linear-quadratic flexo-AFD coupling may contribute significantly to observable interfacial polarization induced by oxygen octahedral rotations at the antiphase boundaries and/or twin walls in YMnO3, Ca3Mn2O7, CaTiO3 and SrTiO3, as well as lead to the appearance of versatile spatially modulated structures in multiferroics [1]. The quadratic dependence of the linear-quadratic flexo-AFD coupling energy on $\vec{\Phi}$ appeared principally important for the emergence of interfacial polarization, because the odd powers of anti-phase (i.e., sign-alternating in neighboring sublattices) pseudovector $\vec{\Phi }$ cannot induce the continuous polarization of structural domain walls, surfaces or interfaces in AFD ferroelastics. Therefore, it seemed that it made little sense to consider odd powers of $\vec{\Phi }$ when constructing the sublattice-insensitive flexo-AFD coupling energy. However, recently Visser et al. [2] and Fang et al. [3] proposed the concept of alterelectricity, an electrical analogue of altermagnetism, in which two switchable states possess alternating band structures. Using the Landau-Ginsburg-Devonshire approach we show that the linear gradient-type coupling between the electric polarization vector $\vec{P}$ and antiferrodistortive long-range order parameter pseudovector $\vec{\Phi }$, that has the form of Lifshitz invariant $\left(\vec{P}\bullet \mathrm{\nabla }\times \vec{\Phi }\; -\vec{\Phi }\bullet \mathrm{\nabla }\times \vec{P}\right)/2$ and named “bilinear flexo-antiferrodistortive coupling”, can emerge in all antiferrodistortive ferroelastics, since it is symmetry-allowed [4]. Using the four sublattices model we reveal that the bilinear flexo-antiferrodistortive coupling can induce the sublattice-sensitive polarization at the twin walls and antiphase boundaries in antiferrodistortive ferroelastics without any ferroelectric or antiferroelectric ordering. Since the induced polarization $\vec{\delta P}$ is perpendicular to $\vec{\Phi}$ and counter-directed in neighboring sublattices with checkerboard-type direction of $\vec{\Phi}$, such structure of $\vec{\delta P}$ may correspond to the alterelectric-type quadrupolar electric order. However, physical manifestations of the bilinear flexo-antiferrodistortive coupling are invisible in most nanostructured antiferrodistortive ferroelectrics and antiferroelectrics due to the domination of piezoelectric and/or omnipresent linear flexoelectric couplings. We have shown that the bilinear flexo-antiferrodistortive coupling can induce alterelectric-type polarization near antiferrodistortive domain boundaries in ferroelastics without any ferroelectric or antiferroelectric long-range ordering [1]. Acknowledgements. The work is primary supported as part of the Computational Materials Sciences Program funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award Number DE-SC0020145. The part of A.N.M. and E.A.E. efforts is also supported by National Academy of Sciences of Ukraine (grants No. 5.8/26-П, 1.4.B/222, III-6-26). [1]. A.N. Morozovska, E.A. Eliseev, M.D. Glinchuk, L.-Q. Chen, V. Gopalan. Interfacial Polarization and Pyroelectricity in Antiferrodistortive Structures Induced by a Flexoelectric Effect and Rotostriction. Phys.Rev. B. 85, 094107 (2012); https://doi.org/10.1103/PhysRevB.85.094107 [2]. A. Visser, V. Könye, O. Janson, J. van den Brink, C. Coulais, and J. van Wezel. "Multipolar Piezoelectricity and Anisotropic Surface Transport in Alterelectrics." arXiv preprint arXiv:2604.18324 (2026); https://doi.org/10.48550/arXiv.2604.18324 [3]. S. Fang, J. Wang, Z. Guo, J. Gong, H. Meng, W. Wang, Z. Cheng, X. Wang, and Y. S. Ang. "Alterelectricity: Electrical Analogue of Altermagnetism." arXiv preprint arXiv:2604.07112 (2026); https://doi.org/10.48550/arXiv.2604.07112 [4]. E. A. Eliseev, A. N. Morozovska, A. Saha and V. Gopalan. Bilinear Flexo-Antiferrodistortive Coupling in Ferroelastics: Polar Twins, Antiphase Boundaries and Fingerprints of Alterelectricity. ArXiv Preprint (2026); https://doi.org/10.48550/arXiv.2606.29456

Competing orders in rhombohedral N-layer graphene (CONDENSED MATTER PHYSICS)

• Sergei Sharapov (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

Room: Conference Hall We investigate the emergence of correlated electron phases in rhombohedral $N$-layer graphene due to two-valley Coulomb interactions within a low-energy $k \cdot p$ framework. Analytical expressions for Lindhard susceptibilities in intra- and intervalley channels are derived, and the critical temperatures for phase transitions are estimated using both the random phase approximation (RPA) and the parquet approximation (PA). Within RPA, only Stoner and intervalley coherent (IVC) phases are supported, while the PA reveals a richer phase structure including particle-particle (PP) channel instabilities. Magnetoelectric control of orbital magnetic order in crystalline rhombohedral hexalayer graphene (R6G) is achieved without introducing a moire superlattice. A hallmark of this magnetic order, which implies time-reversal symmetry breaking, is a finite Hall conductance at zero magnetic field. We observe a non-volatile and hysteretic anomalous Hall effect that can be electrically toggled by sweeping either the carrier density or the displacement field. A model describing this behavior is proposed. A. Herasymchuk, S.G. Sharapov, O.V. Yazyev, Y. Zhumagulov, Phys. Rev. B 113, 035132 (2026)

Spectrum of electron states in a charged atomic chain within the Dirac description (CONDENSED MATTER PHYSICS)

• Alexander Eremko (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

Room: Conference Hall It is demonstrated that the description of electron states in a one-dimensional crystal with account of electron spin should be based on the Dirac theory. Electron spin states are determined by the eigen states of the spinor invariants with their free parameters. It is shown that in the case of atomic chain with the cylindric symmetry integrals of motion include a set of spinor operators corresponding to different spin states. Electrons bound by a charged atomic chain, are shown to attain one-dimensional character of motion and can have arbitrary spin orientation corresponding to the particular chosen spinor invariant. The general solution of the Dirac equation for a one-dimensional crystal is obtained analytically and is shown to be independent of the choice of the spinor invariant(s). It includes free parameters which have the meaning of spin variables and can be fixed corresponding to the concrete spinor invariants determined by the symmetry of the system and experiment conditions. The spectrum of bound electrons in atomic chain is calculated. The electron band structure is shown to be characterized by the principal quantum number *n* so that the corresponding energy bands are split into *n* subbands describing their fine structure.

Is the superfluidity of a Bose gas related to the spontaneous breaking of $U(1)$ symmetry? (CONDENSED MATTER PHYSICS)

• Maksim Tomchenko (Bogolyubov Institute for Theoretical Physics)

Room: Conference Hall It is widely accepted that phonons in a superfluid Bose gas are Goldstone bosons, and that the spontaneous breaking of $U(1)$ symmetry is the primary cause of superfluidity. The first statement is justified by spontaneous symmetry breaking (SSB), which is usually defined as follows: the Hamiltonian of the system is invariant under the $U(1)$ transformation $\hat{\Psi}(\mathbf{r},t)\rightarrow e^{i\alpha}% \hat{\Psi}(\mathbf{r},t)$, but the order parameter $\Psi(\mathbf{r},t)$ is not. However, the strict definition of SSB is different: the Hamiltonian and the boundary conditions are invariant under a symmetry transformation, while the $\it{ground~ state}$ is not. Based on the latter criterion, we study a finite system of spinless, weakly interacting bosons using three approaches: the standard Bogoliubov method, the particle-number-conserving Bogoliubov method, and the approach based on the exact ground-state wave function. Our results show that SSB does not occur in a real-world (finite) superfluid Bose gas. Therefore, the phonons in such a gas are not Goldstone bosons and are similar to sound in a classical gas, and the superfluidity of such a system is not related to the spontaneous breaking of the $U(1)$ symmetry. In the case of an infinite Bose gas, however, the situation becomes paradoxical: the ground state can be regarded as either infinitely degenerate or non-degenerate; this means that the phonon is both similar to a Goldstone boson and different from it. [1] [1] M. Tomchenko, Is a phonon excitation of a superfluid Bose gas a Goldstone boson? J. Phys. A: Math. Theor. 59, 305202 (2026). https://doi.org/10.1088/1751-8121/ae8c94

Field-controlled thermal spin transport in rutile-type altermagnets (QUANTUM MATERIALS)

• Yuliia Gusieva (G.V. Kurdyumov Institute for Metal Physics of the NAS of Ukraine)

Room: Conference Hall The magnon-driven transport properties of a two-dimensional model of a $d$-wave altermagnet are investigated. As a case study, we consider a rutile with easy-planar anisotropy (e.g., $\mathrm{NiF}_2$), where the sublattice magnetization vectors lie within the $xy$-plane in the equilibrium state. An external magnetic field is applied perpendicular to this plane, along the $z$-axis. The model Hamiltonian accounts for anisotropy, Zeeman interaction, and the complex structure of the Heisenberg exchange, including ferromagnetic, antiferromagnetic, and specific altermagnetic exchange contributions. We computed the spectrum of spin waves and found that altermagnetism renders magnons chiral, as in the case of the easy-planar $g$-wave altermagnets [1]. The altermagnetically-induced magnon magnetic moment is $k$-dependent, and its distribution over the 1st Brillouin zone possesses $d$-wave symmetry for each magnon branch. The latter results in a magnon-driven spin current in response to an applied temperature gradient, similar to that in easy-axial $d$-wave altermagnets [2]. The corresponding tensor of the thermal spin conductivity $\sigma_{\alpha\beta}$ was derived from the transport Boltzmann equation within the relaxation time approximation. The direction of the spin current is determined by the direction of the temperature gradient relative to the crystallographic axes (Fig. 1). An important finding of this research is the possibility of controlling the spin conductivity by the applied magnetic field. We observe that at low temperatures, the conductivity is governed by the lowest-energy magnon mode, and its temperature dependence follows a $T^2$-law. However, for high temperatures, $\sigma_{\alpha\beta}$ is temperature-independent, and its value and sign are determined by the magnetic field. The field-controlled spin conductivity highlights the potential for tunable magnonic and spin-caloritronic devices, providing a robust mechanism for controlling spin and heat currents at the nanoscale. **Fig. 1.** Temperature dependencies of $\sigma_{xy}$ for different values of the reduced magnetic field $b = B_z / B_{\mathrm{sf}}$, where $B_{\mathrm{sf}}$ is the critical spin-flip field. This work was supported by the German Federal Ministry of Research, Technology and Space (BMFTR) through the GU-QuMat project (01DK24008). [1] V.P. Kravchuk, et al., *Phys. Rev. B*, **112**, 144421 (2025). [2] K.V. Yershov, et al., *Phys. Rev. B*, **110**, 144421 (2024).

Quantum-Mechanical Analysis of Electron Transport in a Cylindrical Crossed-Field Configuration with a Periodic Boundary Potential (CONDENSED MATTER PHYSICS)

• Dmytro Kadygrob (O. Ya. Usikov Institute for Radio Physics and Electronics of the National Academy of Sciences of Ukraine)

Room: Conference Hall This work presents a fully quantum-mechanical theoretical framework for describing electron dynamics and collective phenomena in a cylindrical crossed-field configuration subject to a spatially periodic boundary potential. The electron cloud is considered in orthogonal radial electric and axial magnetic fields. By solving the Schrödinger equation with the corresponding gauge potentials and an effective radial potential in cylindrical coordinates, we obtain the quantized energy spectrum and spatial structure of the electron states. In the unperturbed state, the quantum-mechanical analysis shows that the radial current vanishes. Electron transport toward the boundary is therefore described as a quantum process associated with transitions between discrete angular-momentum states induced by a spatially inhomogeneous high-frequency field. The periodic boundary potential couples states with different angular momenta and provides a mechanism for phase locking and coherent energy transfer between the electron cloud and the electromagnetic field. A key result of the work is the identification of a mathematical correspondence between the formation of azimuthal space-charge structures, commonly referred to as spokes, and the collective phenomena described by the Landau theory of second-order phase transitions and the Ginzburg–Landau theory. The emergence of rotating electron bunches is interpreted as a spontaneous symmetry-breaking process, while the spokes are described as stable, spatially coherent structures of a complex order parameter. The proposed framework establishes a connection between microscopic quantum electron dynamics and macroscopic order-parameter theory, providing a unified description of electron transport, collective self-organization, phase coherence, and nonlinear evolution of azimuthal space-charge structures in cylindrical crossed-field configurations.