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SUMMARY:Dynamics of correlations of many colliding particles
DTSTART;VALUE=DATE-TIME:20240926T093000Z
DTEND;VALUE=DATE-TIME:20240926T095000Z
DTSTAMP;VALUE=DATE-TIME:20260606T001658Z
UID:indico-contribution-297@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Viktor Gerasimenko (Institute of Mathematics NAS of 
 Ukraine)\nThe talk provides an overview of some advances in the mathematic
 al understanding of the nature of the dynamics of the correlations of many
  colliding particles. The fundamental equations of modern mathematical phy
 sics are studied\, in particular the hierarchies of the evolution equation
 s of many hard spheres and their asymptotic behavior described by kinetic 
 nonlinear equations.\n\nFirst\, an approach to describing correlations in 
 a system of colliding particles interacting as hard spheres is discussed\,
  based on a hierarchy of equations for the evolution of a sequence of corr
 elation functions that are cumulants of distribution functions\, called th
 e Lioville hierarchy. It is proven that the constructed dynamics of correl
 ations underlie the description of the dynamics of both a finite and an in
 finite number of hard spheres obeying the BBGKY hierarchies for reduced (m
 arginal) distribution functions or reduced correlation functions.\n\nThe s
 tructure of expansions representing non-perturbative solutions of the Cauc
 hy problem for these hierarchies of evolution equations is formulated. It 
 has been established that the concept of cumulants of the groups of operat
 ors of the Lioville equations underlies non-perturbative expansions of sol
 utions to the hierarchies of fundamental equations describing the evolutio
 n of observables and of the state of many hard spheres\, as well as forms 
 the basis of the kinetic description of their collective behavior.\n\nIn t
 he talk\, we also consider a new approach to the problem of a rigorous des
 cription of kinetic evolution by means of reduced (marginal) observables g
 overned by the dual BBGKY hierarchy. One of the advantages of the develope
 d approach to the derivation of kinetic equations from the underlying dyna
 mics of many particles is that it provides an opportunity to construct kin
 etic equations with initial correlations\, in particular correlations char
 acterizing the condensed states of a system\, and to describe the processe
 s of the propagation of initial correlations within suitable scaling limit
 s.\n\nReferences\n[1] Gerasimenko V I and Gapyak I V 2023 Advances in theo
 ry of evolution equations of many colliding particles. *Proc. Inst. Math. 
 NASU* **20** 729–804 doi:10.3842/trim.v20n1.528\n[2] Gerasimenko V I and
  Gapyak I V 2022 Propagation of correlations in a hard sphere system. *J S
 tat. Phys.* **189** 2 doi:10.1007/s10955-022-02958-8\n[3] Gerasimenko V I 
 and Gapyak I V 2021 Boltzmann–Grad asymptotic behavior of collisional dy
 namics. *Reviews in Math. Phys.* **33** 2130001 32 doi:10.1142/S0129055X21
 300016\n[4] Gerasimenko V I and Gapyak I V 2019 Processes of creation and 
 propagation\nof correlations in large quantum particle system. In: *Panora
 ma of Contemporary Quantum Mechanics – Concepts and Applications.* Londo
 n: InTech\, 2019 doi:10.5772/intechopen.82836\n\nhttps://indico.bitp.kiev.
 ua/event/13/contributions/297/
LOCATION:Bogolyubov Institute for Theoretical Physics (Section 1-4)\, Inst
 itute of Mathematics (Section 5) 322
URL:https://indico.bitp.kiev.ua/event/13/contributions/297/
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