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

Abstract

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