Electrical conductivity of charged particle systems and the Zubarev NSO method

TL;DR

This paper reviews Zubarev's NSO method for nonequilibrium statistical mechanics, focusing on electrical conductivity in charged particle systems, and discusses theoretical aspects, correlations, and open questions.

Contribution

It provides a systematic treatment of electrical conductivity using the NSO method and Green functions, highlighting the relation to kinetic and response theories.

Findings

Comparison of different conductivity expressions

Discussion of correlation functions and convergence issues

Identification of open questions in the theory

Abstract

One of the fundamental problems in physics which are not rigorously solved yet is the statistical mechanics of nonequilibrium processes. An important contribution to describe irreversible behavior starting from reversible Hamiltonian dynamics was given by D. N. Zubarev who invented the method of the nonequilibrium statistical operator (NSO). We discuss this approach, in particular the extended von Neumann equation, and consider as example the electrical conductivity of a charged particle system. The selection of the set of relevant observables is considered. The relation between kinetic theory and linear response theory is shown. Using thermodynamic Green functions, a systematic treatment of correlation functions is given, but convergence has to be investigated. Different expressions for the conductivity are compared, and open questions are identified.