Refined Weak Coupling Limit: Coherence, Entanglement and Non-Markovianity

TL;DR

This paper introduces a refined weak coupling approach that accurately captures non-Markovian effects in the spin-boson model, revealing new phenomena such as coherence revivals and persistent non-divisibility.

Contribution

It develops a complete positivity-preserving weak coupling limit that enables exact derivation of a master equation with reversible energy exchange, unveiling novel non-Markovian behaviors.

Findings

Coherence exhibits revivals while entanglement does not.

The dynamics show 'quasieternal' non-Markovianity with non-divisibility at all times.

An exact master equation with a time-dependent Lamb shift is derived.

Abstract

We study the properties of a refined weak coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system presents a rich and new non-Markovian phenomenology. This implies a dynamical difference between entanglement and coherence: the latter undergoes revivals whereas the former not, despite the induced dynamics being fully incoherent. In addition, the evolution presents "quasieternal" non-Markovianity, becoming non-divisible at any time period where the system evolves qualitatively. Furthermore, the method allows for an exact derivation of a master equation that accounts for a reversible energy exchange between system and environment. Specifically, this is obtained in the form of a time-dependent Lamb shift term.