Optimally chosen Nakajima-Zwanzig master equation for mean field approximation

TL;DR

This paper introduces an optimized mean field approach to the Nakajima-Zwanzig master equation for quantum open systems, providing a new way to derive inhomogeneous non-Markovian dynamics with proven positivity and equilibration.

Contribution

It develops a method to select optimal projection operators for deriving inhomogeneous master equations with improved properties in quantum open systems.

Findings

Extended proofs of positivity and equilibration to new equations

Applied method to nitrogen vacancy centers in diamond

Demonstrated improved modeling of non-Markovian effects

Abstract

We define an ensemble of projection operators, each of which has an exact associated Nakajima-Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields, for an optimally chosen projection operator, a completely determined inhomogeneous master equation. Previous proofs of positivity and equilibration are extended to these new inhomogeneous non-Markovian master equations. We study a nitrogen vacancy center in diamond interacting with 13C impurities to illustrate the method.