Decoherence in open quantum systems: influence of the intrinsic bath dynamics

TL;DR

This paper derives a non-Markovian master equation for open quantum systems incorporating intrinsic bath dynamics, using a generalized projection technique, and validates it through comparison with exact solutions in a dephasing model.

Contribution

It introduces a generalized Zwanzig-Nakajima projection method that accounts for intrinsic bath dynamics, extending the standard approach for non-Markovian quantum systems.

Findings

The derived kinetic equation includes a nonlinear term related to bath dynamics.

The approach is consistent and robust when applied to a simple dephasing model.

Comparison with exact solutions confirms the validity of the generalized equation.

Abstract

The non-Markovian master equation for open quantum systems is obtained by generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath $\varrho_{B}(t)$ and of the system $\varrho_{S}(t)$ are written. Formal solution of the equation for $\varrho_{B}(t)$ in the 2-nd approximation in interaction yields a specific extra term, related to the intrinsic bath dynamics. This term is nonlinear in the reduced density matrix $\varrho_{S}(t)$, and vanishes in the Markovian limit. To verify the consistence and robustness of our approach, we apply the generalized ZN projection scheme to a simple dephasing model. We study the obtained kinetic equation both in the Markovian approximation and beyond it (for the term related to the intrinsic bath dynamics) and compare the results with the exact ones.