Statistical quasi-particle theory for open quantum systems

ABSTRACT

This paper presents a comprehensive account on the recently developed dissipaton–equation–of–motion (DEOM) theory. This is a statistical quasi-particle theory for quantum dissipative dynamics. It accurately describes the influence of bulk environments, with a few number of quasi-particles, the dissipatons. The novel dissipaton algebra is then followed, which readily bridges the Schrödinger equation to the DEOM theory. As a fundamental theory of quantum mechanics in open systems, DEOM characterizes both the stationary and dynamic properties of system–and–bath interferences. It treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that could be experimentally measurable. Examples are the linear or nonlinear Fano interferences and the Herzberg–Teller vibronic couplings in optical spectroscopies. This review covers the DEOM construction, the underlying dissipaton algebra and theorems, the physical meanings of dynamical variables, the possible identifications of dissipatons, and some recent advancements in efficient DEOM evaluations on various problems. The relations of the present theory to other nonperturbative methods are also critically presented.

KEYWORDS:

• System-and-bath entanglement
• second-quantization
• generalised Wick's theorem
• generalised diffusion equation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The support from the Ministry of Science and Technology [grant number 2016YFA0400900], [grant number 2016YFA0200600]; Natural Science Foundation of China [grant number 21233007], [grant number 21373191], [grant number 21573202], [grant number 21633006], [grant number 21703225]; Fundamental Research Funds for the Central Universities [grant number 2030020028], [grant number 2340000074], [grant number 2060030025]; Anhui Provincial Natural Science Foundation [grant number 1708085QB30] is gratefully acknowledged.