A time-dependent regularization of the Redfield equation

TL;DR

This paper proposes a novel time-dependent regularization method for the Redfield equation that maintains complete positivity and improves transient dynamics modeling in open quantum systems.

Contribution

It introduces a regularization technique replacing the Kossakowski matrix with its closest positive semidefinite form, preserving time dependence and enhancing accuracy.

Findings

Outperforms partial secular and universal Lindblad equations during transient evolution

Maintains complete positivity and divisibility of quantum processes

Uses Choi-Jamiolkowski isomorphism for unbiased comparison

Abstract

We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the time dependence of the Kossakowski matrix, leading to a completely positive divisible quantum process. Using the dynamics of an exactly-solvable three-level open system as a reference, we show that our approach performs better during the transient evolution, if compared to other approaches like the partial secular master equation or the universal Lindblad equation. To make the comparison between different regularization schemes independent from the initial states, we introduce a new quantitative approach based on the Choi-Jamiolkowski isomorphism.