Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory versus core-system hierarchy construction

Abstract

Quadratic system-bath coupling term plays a critical role in many real-world physical models. To treat the quadratic coupling term exactly, we have developed the generalized dissipaton-equations-of-motion (DEOM) method and stochastic-fields-dressed DEOM (SFD-DEOM) method. Among them, the generalized DEOM needs to be scrutinized and SFD-DEOM has many restrictions in the application. In this article, we combine the traditional DEOM theory with the Fokker-Planck algebra. The resulting Fokker-Planck quantum master equation (FP-QME) is an exact dynamical master equation for open quantum systems, and can be directly applied to non-linear system-bath coupling cases. We scrutiny those three methods and the results witness the establishment of the exact theory and numerical method of the open quantum system under quadratic system-bath coupling.