A Hierarchical-Equation-of-Motion Based Semiclassical Approach to Quantum Dissipation^†

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 effects of system-bath couplings. The SC-HEOM methodology is exemplified in this work on the hierarchical quantum master equationJ. Chem. Phys. 131 , 214111 (2009) and numerically demonstrated on linear spectra of anharmonic oscillators.