As a system can be separated from its heat bath via a decoupling scheme based on the Hubbard-Stratonovich transformation, the quantum dissipative dynamics is exactly described by the average of the random system moving in the stochastic field induced by the bath. As a test of this stochastic formalism, a direct numerical implementation is employed to simulate the spontaneous decay of a two-state atom. In contrast, the validity of a deterministic algorithm based on the stochastic scheme is investigated. Moreover, a mixed random-deterministic approach is established and its efficiency is exemplified by studying the exact dynamics for the spin-boson model at zero temperature.

The zero-temperature dynamics of the spin-boson model with strong dissipation has been a challenging problem for more than 20 years. To solve this and quantum dynamics of dissipative systems at large, we recently proposed a mixed random-deterministic method. This scheme has been successfully used to simulate the time evolution of the spin-boson model at zero temperature for weak to moderate dissipation. For a better numerical performance, the approach is further modified so that it is flexible to convert a certain part of the random treatment to a deterministic one a la hierarchical equations. Applying the new method to the strong dissipated spin-boson model at zero temperature, we observe that the population in the localized state obeys a simple decay dynamics and the time scale is proportional to the reciprocal of the cutoff frequency.

No abstract