Computable form of the Born-Markov master equation for open multilevel quantum systems

Abstract

The Redfield and Lindblad forms of the master equations are obtained under not only the Born and Markov approximations but also the secular approximation. In this paper, we propose a computable form of the master equation for open multilevel quantum systems beyond the secular approximation. The proposed form can retain some dynamical effects that are lost due to use of the secular approximation. Two kinds of open multilevel quantum systems are investigated by using this method, and the results are compared to the ones obtained from the Redfield equation and an exactly numerical path integral approach. It is shown that the results obtained from this computable form match those from the exact numerical path integral approach better than results from the Redfield equation. The normal-diffusion coefficient, momentum-damping coefficient, anomalous-diffusion coefficient, etc. in the master equation are also reevaluated.