Non-Markovian correlation functions for open quantum systems

TL;DR

This paper introduces a general formula for non-Markovian correlation functions in open quantum systems, extending the quantum regression theorem to account for memory effects and short-time dynamics.

Contribution

It provides a novel approach transforming time-nonlocal master equations into time-local equations, enabling easier calculation of non-Markovian correlations.

Findings

Derived a simple, practical formula for non-Markovian correlation functions.

Demonstrated the method on quantum dot current fluctuations.

Showed non-Markovian effects are significant at short times.

Abstract

Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the conventional time-nonlocal master equation into dispersed time-local equations-of-motion. The validity of our approximations is discussed and we find that the non-Markovian terms have to be included for short times. While calculations of the density matrix at short times suffer from the initial value problem, a correlation function has a well defined initial state. The resulting formula for the non-Markovian correlation function has a simple structure and is as convenient in its application as the conventional quantum regression theorem for the Markovian case. For illustrations, we apply our method to investigate the spectrum of the current fluctuations of interacting quantum dots contacted with two electrodes. The corresponding non-Markovian characteristics are demonstrated.