Eur. Phys. J. Special Topics 227, 1849–1867 (2019)
https://doi.org/10.1140/epjst/e2018-800047-4

Review

Exact master equation and general non-Markovian dynamics in open quantum systems^★

Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan

^a e-mail: wzhang@mail.ncku.edu.tw

Received: 11 April 2018
Received in final form: 3 July 2018
Published online: 18 January 2019

Abstract

Investigations of quantum and mesoscopic thermodynamics force one to answer two fundamental questions associated with the foundations of statistical mechanics: (i) how does macroscopic irreversibility emerge from microscopic reversibility? (ii) how does the system relax in general to thermal equilibrium with its environment? The answers to these questions rely on a deep understanding of nonequilibrium decoherence dynamics of systems interacting with their environments. Decoherence is also a main concern in developing quantum information technology. In the past two decades, many theoretical and experimental investigations have devoted to this topic, most of these investigations take the Markov (memory-less) approximation. These investigations have provided a partial understanding to several fundamental issues, such as quantum measurement and the quantum-to-classical transition, etc. However, experimental implementations of nanoscale solid-state quantum information processing makes strong non-Markovian memory effects unavoidable, thus rendering their study a pressing and vital issue. Through the rigorous derivation of the exact master equation and a systematical exploration of various non-Markovian processes for a large class of open quantum systems, we find that decoherence manifests unexpected complexities. We demonstrate these general non-Markovian dynamics manifested in different open quantum systems.