Rui-Xue Xu, Yang Liu, Hou-Dao Zhang, YiJing Yan*
Quantum dissipation plays crucial roles in many fields of modern science. Almost all existing quantum dissipation theories, from the perturbative quantum master equations to the exact Feynman--Vernon influence functional path integral and its differential hierarchical equations of motion approaches, exploit the Gaussian-Wick's theorem in thermodynamical statistics. As it is strictly valid only for linear bath couplings, the Gaussian-Wick's theorem treats intrinsically a weak backaction of system on environment.
In this work we propose a generalized Wick’s theorem to treat nonlinear coupling environments that are non-Gaussian. Proposed also is a statistical quasi-particle picture, in which the influence of environments of infinite degrees of freedom is accurately described with a finite number quasi-particles (dissipatons). The novel dissipaton algebra readily bridges the Schrödinger equation to the dissipaton-equation-of-motion (DEOM) theory as a fundamental theory of quantum mechanics in open systems. To validate the new ingredient of the underlying dissipaton algebra, we derive an extended Zusman equation for quadratic bath couplings, via a totally different approach. We prove that the new theory, if it starts with the identical setup, constitutes the dynamical resolutions to the extended Zusman equation. In this way, the generalized (non-Gaussian) Wick's theorem with dissipatons--pair added is verified. This new algebraic ingredient enables the dissipaton approach being naturally extended to high-order nonlinear coupling environments. Moreover, it is noticed that, unlike the linear bath coupling cases, the influence of a non-Gaussian environment cannot be completely characterized with the linear response theory. The new theory has to take this fact into account. The developed DEOM theory manifests the dynamical interplay between dissipatons and nonlinear bath coupling descriptors which are specified in this work. Numerical demonstrations are given with the optical line shapes in a quadratic coupling environment.