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SUMMARY:Propagation of correlations in quantum systems of many particles a
 nd kinetic equations
DTSTART;VALUE=DATE-TIME:20260924T073000Z
DTEND;VALUE=DATE-TIME:20260924T075000Z
DTSTAMP;VALUE=DATE-TIME:20260914T061815Z
UID:indico-contribution-502@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Viktor Gerasimenko (Institute of mathematics NAS of 
 Ukraine)\nThe talk provides an overview of recent progress in the mathemat
 ical understanding \nof kinetic equations that govern quantum systems with
  many particles.\n\nThe talk will begin by discussing an approach to descr
 ibing the evolution of correlations in systems of many quantum particles. 
 This method is based on the von Neumann hierarchy of evolution equations f
 or a sequence of correlation operators or cumulants of the density operato
 rs. It will be proved that the constructed dynamics of correlations underl
 ie the description of the evolution of the state\, both for finitely and i
 nfinitely many quantum particles\, governed by the BBGKY hierarchy for red
 uced density operators or by the hierarchy of nonlinear evolution equation
 s for reduced correlation operators.\n\nFurthermore\, this discussion will
  demonstrate that the concept of cumulants of the groups of operators for 
 the von Neumann equations underlies nonperturbative solutions to hierarchi
 es 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.\n\nThe 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 dyna
 mics of many particles is the ability to construct kinetic equations that 
 incorporate initial correlations and to describe the processes of propagat
 ing these initial correlations under appropriate scaling approximations.\n
 \n\nReferences\n\n[1] Gerasimenko\, V.I. Hierarchies of quantum evolution 
 equations and dynamics of many-particle correlations\, in: Statistical Mec
 hanics and Random Walks: Principles\, Processes and Applications\, N.Y.: N
 ova Sci. Publ.\, Inc.\, 2013\, 233-288.\n[2] Gerasimenko\, V.I.\, Gapyak\,
  I.V. Cumulant expansions of operator groups of quantum many-particle syst
 ems. Ukrainian Math. J. 78(3-4) 218-234 (2026). doi:10.3842/umzh.v78i3-4.9
 375\n[3] Gerasimenko\, V.I. The Heisenberg picture of quantum kinetic evol
 ution in the mean-field limit. Kinetic & Related Models. 4(1) 385-399 (201
 1). doi:10.3934/krm.2011.4.385\n[4] Gerasimenko V.I.\, Gapyak I.V. Propaga
 tion of correlations in a hard-sphere system. J Stat. Phys. 189(2)\, (2022
 ). doi:10.1007/s10955-022-02958-8\n[5] Gerasimenko\, V.I.\, Gapyak\, I.V. 
 Boltzmann-Grad asymptotic behavior of collisional dynamics. Reviews in Mat
 h. Phys. 33 2130001 32 (2021). doi:10.1142/S0129055X21300016\n\nhttps://in
 dico.bitp.kiev.ua/event/18/contributions/502/
LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall
URL:https://indico.bitp.kiev.ua/event/18/contributions/502/
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