Exploring complete positivity in hierarchy equations of motion

TL;DR

This paper develops an algebraic framework to identify hierarchy equations of motion that guarantee completely positive quantum dynamics, providing bounds on violations and constructing models with non-Markovian coherence revivals.

Contribution

It introduces a novel algebraic method for ensuring complete positivity in hierarchy equations of motion and demonstrates its practical applicability with multiple examples.

Findings

Bounds on violation of complete positivity established

Constructed models with non-Markovian quantum coherence revivals

Applicable to microscopically derived hierarchy equations

Abstract

We derive a purely algebraic framework for the identification of hierarchy equations of motion that induce completely positive dynamics and demonstrate the applicability of our approach with several examples. We find bounds on the violation of complete positivity for microscopically derived hierarchy equations of motion and construct well-behaved phenomenological models with strongly non-Markovian revivals of quantum coherence.