Generalized Kinetic and Evolution Equations in the Approach of the Nonequilibrium Statistical Operator

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.

Two-Temperature Model of Nonequilibrium Electron Relaxation: A Review

“…So, only the collsion term is important in the Boltzmann transport equation, which has two contributions; phonon generation or phonon absorption when electron scatters from one state to another. For a general discussion of the applicability of the Boltzmann kinetic equation in quantum cases see the review article by A. L. Kuzemsky 18 . The transition rate (probability/second) of an electron scattering from a state k to state k ′ with a phonon generation of energyhω f is W (k ′ |k)δ(ε k ′ − ε k −hω), and for phonon absorption, transition rate is W (k|k…”

Electronic Transport in Metallic Systems and Generalized Kinetic Equations

“…The kinetic equations are of great interest in the theory of transport processes. In the NSO approach, 42,45,307 the main quantities involved are the following thermodynamically conjugate values:…”

“…In Ref. 307 we described a kind of general formalism for the calculation of transport coefficients which includes the approaches discussed above and which can be adapted to the problem investigated.…”

Statistical Theory of Spin Relaxation and Diffusion in Solids

“…On this basis we have derived, by statistical mechanics methods, the kinetic equations for a system weakly coupled to a thermal bath. 64 Our motivation for presenting this alternative derivation is based on the conviction that the NSO method provides some advantages in displaying the physics of the relaxation processes.…”