Lindblad equation and its semiclassical limit of the Anderson-Holstein model

For multi-level open quantum systems, the interaction between different levels could pose a challenge to understand the quantum system both analytically and numerically. In this work, we study the approximation of the dynamics of the Anderson-Holstein model, as a model of the multi-level open quantum system, by Redfield and Lindblad equations. Both equations have a desirable property that if the density operators for different levels are diagonal initially, they remain to be diagonal for any time. Thanks to this nice property, the semiclassical limit of both Redfield and Lindblad equations could be derived explicitly; the resulting classical master equations share similar structures of transport and hopping terms. The Redfield and Lindblad equations are also compared from the angle of time dependent perturbation theory.

Duke Scholars

Author Jianfeng Lu Mathematics