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Bogoliubov-Born-Green-Kirkwood-Yvon chain and kinetic equations for the level dynamics in an externally perturbed quantum system
journal contribution
posted on 2017-06-05, 14:13 authored by Mumu Qureshi, Johnny Zhong, Joseph BetourasJoseph Betouras, Alexandre ZagoskinAlexandre ZagoskinTheoretical description and simulation of large quantum coherent systems out of equilibrium remains a daunting task. Here we are developing a new approach to it based on the Pechukas-Yukawa formalism, which is especially convenient in case of an adiabatically slow external perturbation. In this formalism the dynamics of energy levels in an externally perturbed quantum system as a function of the perturbation parameter is mapped on that of a fictitious one-dimensional classical gas of particles with cubic repulsion. Equilibrium statistical mechanics of this Pechukas gas allows to reproduce the random matrix theory of energy levels. In the present work, we develop the nonequilibrium statistical mechanics of the Pechukas gas, starting with the derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of equations for the appropriate generalized distribution functions. Sets of approximate kinetic equations can be consistently obtained by breaking this chain at a particular point (i.e. approximating all higher-order distribution functions by the products of the lower-order ones). When complemented by the equations for the level occupation numbers and inter-level transition amplitudes, they allow to describe the nonequilibrium evolution of the quantum state of the system, which can describe better a large quantum coherent system than the currently used approaches. In particular, we find that corrections to the factorized approximation of the distribution function scale as 1/N, where N is the number of the "Pechukas gas particles" (i.e. energy levels in the system).
Funding
This work has been supported by EPSRC through the Grant No. EP/M006581/1.
History
School
- Science
Department
- Physics
Published in
Physical Review AIssue
95Citation
QURESHI, M.A. ...et al., 2017. Bogoliubov-Born-Green-Kirkwood-Yvon chain and kinetic equations for the level dynamics in an externally perturbed quantum system. Physical Review A, 95, 032126.Publisher
© American Physical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2017-02-28Publication date
2017-03-22Notes
This paper was accepted for publication in the journal Physical Review A and the definitive published version is available at http://dx.doi.org/10.1103/PhysRevA.95.032126ISSN
2469-9934Publisher version
Language
- en