Lindblad equation and its semi-classical limit of the Anderson-Holstein model

Abstract

For multi-level open quantum system, the interaction between different levels could pose 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 multi-level open quantum system, by Redfield and Lindblad equations. Both equations have a desirable property that if the density operators for different levels is diagonal initially, they remain to be diagonal for any time. Thanks to this nice property, the semi-classical 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.

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Cited by in corpus (5)

• Mpemba effects in open nonequilibrium quantum systems
• Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems
• Efficient Frozen Gaussian Sampling Algorithms for Nonadiabatic Quantum Dynamics at Metal Surfaces
• Markovian Embedding Procedures for Non-Markovian Stochastic Schrödinger Equations
• Stochastic Schrödinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective