By Jiushu Shao
Beijing Normal University, Beijing 100875, China

A quantum analogue of the traditional Brownian motion has been established for dissipative systems described by the system-plus-bath model. It is shown that the evolution of the system or the reduced density matrix satisfies a stochastic Liouville equation driven by complex noises. As a theoretical tool this stochastic formulation can be used to derive both approximate master equations and exact ones for specific systems. It can also be employed as a practical technique for simulating nonequilibrium dynamics numerically via a direct implementation or transforming to a deterministic algorithm a la hierarchical equations. It has been demonstrated that a mixed random-deterministic scheme allows us to calculate the zero-temperature dynamics of the spin-boson model with Ohmic dissipation. It is found that for strong dissipation the population in the localized state obeys a simple rate dynamics and time scale is proportional to the reciprocal of the cutoff frequency. This observation still awaits for further theoretical explanation.

*Supported by the National Natural Science Foundation and the Ministry of Science and Technology, China