Theory of quantum dissipation in a class of non-Gaussian environments

TL;DR

This paper develops a new dissipaton-equation-of-motion (DEOM) theory for non-Gaussian environments with quadratic bath coupling, extending the algebraic framework and validating it through an extended Zusman equation, with numerical applications to optical line shapes.

Contribution

It introduces a novel DEOM framework for nonlinear, non-Gaussian environments based on an extended algebraic approach, validated by deriving an extended Zusman equation.

Findings

Validated the new DEOM with the extended Zusman equation.

Extended the dissipaton algebra to nonlinear bath couplings.

Numerical results on optical line shapes in quadratic environments.

Abstract

In this work we construct a novel dissipaton-equation-of-motion (DEOM) theory in quadratic bath coupling environment, based an extended algebraic statistical quasi-particle approach. To validate the new ingredient of the underlying dissipaton algebra, we derive an extended Zusman equation 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. Thus, we verify the generalized (non-Gaussian) Wick's theorem with dissipatons-pair added. This new algebraic ingredient enables the dissipaton approach being naturally extended to nonlinear coupling environments. Moreover, it is noticed that, unlike the linear bath coupling case, 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 that will be specified. Numerical demonstrations will be given with the optical line shapes in quadratic coupling environment.