Theory of Transport Coefficients. I. General Theory and Electrical Conductivity of Electron-Phonon System

Abstract

A general method is presented for the calculation of static transport coefficients based on Kubo's formulas. Techniques of perturbation expansion, diagram representation, and linked‐cluster expansion are used. As an example, the electrical conductivity of an electron‐phonon system is calculated with the natural introduction of irreversibility, following the ideas of Van Hove, and Prigogine and his collaborators. Under certain conditions the present method is shown to be equivalent to the conventional method by means of the Boltzmann equation. These conditions are examined and the improvement of the approximation is discussed.