Transport equations including many-particle correlations for an arbitrary quantum system. General formalism

TL;DR

This paper introduces a novel method for deriving transport equations in quantum many-particle systems, utilizing an equation-of-motion approach and cluster expansions to handle arbitrary interactions and external fields.

Contribution

The paper presents a systematic hierarchy-breaking technique for quantum transport equations using correlation expansions, applicable to both bosons and fermions with arbitrary interactions.

Findings

Method applicable to systems with arbitrary interactions and external fields

Derivation of diagrammatic representations for transport equations

Validation through application to exactly soluble models in a subsequent study

Abstract

We present a new method to derive transport equations for quantum many-particle systems. This method uses an equation-of-motion technique and is applicable to systems with bosons and fermions, arbitrary interactions and time-dependent external fields. Using a cluster expansion of the r-particle density matrices the infinite hierarchy of equations of motion for many-particle expectation values is transposed into an equivalent one in terms of correlations. This new hierarchy permits a systematic breaking of the hierarchy at any order. Diagrams are derived for these transport equations. In a second paper the method is tested for exactly soluble electron-phonon models in one dimension.