Functional Integral approach to time-dependent heat exchange in open quantum systems: general method and applications

TL;DR

This paper develops a path integral method to analyze time-dependent heat exchange in driven quantum systems coupled to thermal reservoirs, providing a comprehensive framework from classical to quantum regimes.

Contribution

It introduces an exact influence functional and formal expression for heat statistics in open quantum systems, applicable to general linear dissipation and time-dependent driving.

Findings

Derived a convolution integral for heat transfer involving system correlations.

Solved the integral in weak-damping limit for white and colored noise.

Discussed quantum effects and achieved a complete description from classical to quantum regimes.

Abstract

We establish the path integral approach for the time-dependent heat exchange of an externally driven quantum system coupled to a thermal reservoir. We derive the relevant influence functional and present an exact formal expression for the moment generating functional which carries all statistical properties of the heat exchange process for general linear dissipation. The general method is applied to the time-dependent average heat transfer in the dissipative two-state system. We show that the heat can be written as a convolution integral which involves the population and coherence correlation functions of the two-state system and additional correlations due to a polarization of the reservoir. The corresponding expression can be solved in the weak-damping limit both for white noise and for quantum mechanical coloured noise. The implications of pure quantum effects are discussed. Altogether a complete description of the dynamics of the average heat transfer ranging from the classical regime down to zero temperature is achieved.