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Dissipation equation of motion approach to open quantum systems

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Abstract

This paper presents a comprehensive account of the dissipaton-equation-of-motion (DEOM) theory for open quantum systems. This newly developed theory treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that are also experimentally measurable. Despite the fact that DEOM recovers the celebrated hierarchical-equations-of-motion (HEOM) formalism, these two approaches have some fundamental differences. To show these differences, we also scrutinize the HEOM construction via its root at the influence functional path integral formalism. We conclude that many unique features of DEOM are beyond the reach of the HEOM framework. The new DEOM approach renders a statistical quasi-particle picture to account for the environment, which can be either bosonic or fermionic. The review covers the DEOM construction, the physical meanings of dynamical variables, the underlying theorems and dissipaton algebra, and recent numerical advancements for efficient DEOM evaluations of various problems. We also address the issue of high-order many-dissipaton truncations with respect to the invariance principle of quantum mechanics of Schrödinger versus Heisenberg prescriptions. DEOM serves as a universal tool for characterizing of stationary and dynamic properties of system-and-bath interferences, as highlighted with its real-time evaluation of both linear and nonlinear current noise spectra of nonequilibrium electronic transport.

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Authors and Affiliations

  1. Hefei National Laboratory for Physical Sciences at the Microscale, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), University of Science and Technology of China, Hefei, 230026, China

    YiJing Yan

  2. Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China

    YiJing Yan

  3. Department of Physics, Hangzhou Normal University, Hangzhou, 310036, China

    Jinshuang Jin

  4. Hefei National Laboratory for Physical Sciences at the Microscale, Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China

    Rui-Xue Xu & Xiao Zheng

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  1. YiJing Yan
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Correspondence to YiJing Yan.

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Yan, Y., Jin, J., Xu, RX. et al. Dissipation equation of motion approach to open quantum systems. Front. Phys. 11, 110306 (2016). https://doi.org/10.1007/s11467-016-0513-5

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