Stochastic simulation of anharmonic dissipation. I. Linear response regime.

Over decades, the theoretical study of the quantum dissipative dynamics was mainly based on the linear dissipation model. The study of the nonlinear dissipative dynamics in condensed phases, where there exist an infinite number of bath modes, is extremely difficult even if not impossible. This work put forward a stochastic scheme for the simulation of the nonlinear dissipative dynamics. In the linear response regime, the second-order cumulant expansion becomes exact to reproduce the effect of the bath on the evolution of the reduced system. Consequently, a Hermitian stochastic Liouville equation is derived without explicit treatment of the bath. Stochastic simulations for an anharmonic model illustrate that the dynamics dissipated by anharmonic bath exhibits substantial difference on temperature dependence compared to that with the Caldeira-Leggett model.