Non-Markovian correlation functions for open quantum systems

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.

11 pages, 5 figures

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Cited by in corpus (6)

• Memory effect preserved time-local approach to noise spectrum of transport current
• Nonlinear optical spectroscopy of open quantum systems
• Phase-controlled quantum transport signatures in a quantum dot-Majorana hybrid ring system
• Distinguishing Majorana bound states from Andreev bound states through differential conductance and current noise spectrum
• Two-time correlation functions beyond quantum regression theorem: Effect of external noise
• Theory of non-Markovian dynamics in resonance fluorescence spectrum