Quantum Diffusion with Drift and the Einstein Relation II

TL;DR

This paper provides technical proofs for the analysis of quantum particle diffusion and drift under thermal reservoirs, focusing on asymptotic perturbation theory and correlation functions, complementing a companion paper.

Contribution

It introduces new technical results including an asymptotic perturbation theory for small driving and the construction of time-dependent correlation functions in quantum diffusion.

Findings

Asymptotic perturbation theory applicable for small driving

Construction of time-dependent correlation functions

Supports analysis of long-time quantum diffusion and drift

Abstract

This paper is a companion to 'Quantum Diffusion with Drift and the Einstein Relation I' (jointly submitted to arXiv). Its purpose is to describe and prove a certain number of technical results used in 'Quantum Diffusion with Drift and the Einstein Relation I', but not proven there. Both papers concern long-time properties (diffusion, drift) of the motion of a driven quantum particle coupled to an array of thermal reservoirs. The main technical results derived in the present paper are $(1)$ an asymptotic perturbation theory applicable for small driving, and, $(2)$ the construction of time-dependent correlation functions of particle observables.