The Lindblad and Redfield forms derived from the Born-Markov master equation without secular approximation and their applications

In this paper, we derive the Lindblad and Redfield forms of the master equation based on the Born-Markov master equation with and without the secular approximation for open multi-level quantum systems. The coefficients of the equations are re-evaluated according to the scheme in [(2019), Phys. Rev. A 99, 022118]. They are complex numbers rather than the real numbers obtained from traditional simplified methods. The dynamics of two models (one is an open three-level quantum system model, and the other is the model of phycoerythrin 545 (PE545) in a photosynthesis system) are studied. It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments, but a large distortion of the dynamics in others. These effects are discussed and characterized by studying the dynamics of nontrivial instances of multi-level systems in the presence of dissipation.

Automated summary

This paper derives the Lindblad and Redfield forms of the master equation based on the Born-Markov master equation, with coefficients re-evaluated as complex numbers rather than real numbers. Dynamics of two models are studied, showing that different environments may cause small or large distortions in dynamics due to the secular approximation and simplified real coefficients. The effects are discussed by studying the dynamics of multi-level systems in the presence of dissipation.