We present a semiclassical （SC） approach for quantum dissipative dynamics, constructed on basis of the hierarchical-equation-of-motion （HEOM） formalism. The dynamical components considered in the developed SC-HEOM are wavepackets＇ phase-space moments of not only the primary reduced system density operator but also the auxiliary density operators （ADOs） of HEOM. It is a highly numerically efficient method, meanwhile taking into account the high-order effcts of system-bath couplings. The SC-HEOM methodology is exemplified in this work on the hierarchical quantum master equation [J. Chem. Phys. 131, 214111 （2009）] and numerically demonstrated on linear spectra of anharmonic oscillators.
Rui-xue XuXue-cheng TaoYao WangYang LiuHou-dao ZhangYiJing Yan
In this work we construct a novel dissipaton-equation-of-motion （DEOM） theory in quadratic bath coupling environment, based on 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.
