Derivation of exact master equation with stochastic description: Models   in quantum optics
  The methodology of stochastic description for dissipation, a generic scheme to decouple the interaction between two subsystems, is applied to the study of dissipative dynamics in quantum optics. It is shown that the influence of the coupled thermal or vacuum field on the quantum mode can be exactly represented by the induced stochastic fields. The quantum mode thereby satisfies a stochastic differential equation and dissipation effect due to the coupling with the environment is obtained through statistical averaging. Within the framework of stochastic description, it is demonstrated how to derive the master equation for a single optical mode interacting with the bosonic bath. A numerical algorithm for solving the master equation in which the coefficients are determined by a set of integral equations is discussed and a comparison with the known results is displayed. The derivation of the master equation for the spontaneous decay of two-state atoms in the vacuum is also presented. 
Haifeng Li and Jiushu Shao
quant-ph