Generalized kinetic and evolution equations in the approach of the nonequilibrium statistical operator

TL;DR

This paper employs the nonequilibrium statistical operator method to derive generalized transport and kinetic equations, elucidating relaxation processes and the emergence of irreversible behavior in quantum systems with weak subsystem interactions.

Contribution

It introduces a formalism that derives generalized kinetic equations, including known equations like magnon and phonon kinetics, from the nonequilibrium statistical operator approach.

Findings

Derived generalized kinetic equations for weakly coupled systems.

Showed the functional similarity of collision terms across different systems.

Connected the formalism to known equations like Peierls and magnon kinetics.

Abstract

The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyse and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrodinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analysed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.