Effective master equations for two accelerated qubits

TL;DR

This paper develops a new Markovian master equation approach for two accelerating Unruh-DeWitt detectors, ensuring complete positivity without RWA, and clarifies the limits of validity for such approximations in open quantum systems.

Contribution

It introduces a revised Markovian approximation that guarantees complete positivity without RWA and analyzes its validity in the context of accelerated detectors.

Findings

The new Markovian limit ensures complete positivity without RWA.

Standard derivations may violate complete positivity outside their validity domain.

Certain regimes, like stacked trajectories or high gap-to-acceleration ratios, invalidate the Markovian approximation.

Abstract

We revisit the problem involving two constantly accelerating Unruh-DeWitt detectors using Open Effective Field Theory methods. We study the time evolution of the joint detector state using a Markovian approximation which differs from the standard one taken in the literature. We show that this Markovian limit already implies the complete positivity of the dynamical evolution map without invoking the rotating wave approximation (RWA), in contrast to standard derivations of open system master equations. By calculating explicitly the domain of validity of this Markovian approximation, we argue that the lack of complete positivity in the usual microscopic derivation stems from the (subtle) fact that the Redfield equation is used outside its domain of validity. We give two well-known cases studied in the literature that violate the validity of the Markovian approximation: (i) the ``stacked trajectory'' limit (when detector trajectories are taken to be on top of one another), and (ii) large gap-to-acceleration ratio. Since Markovian dynamics with or without RWA can lead to different qualitative predictions for entanglement dynamics, our work emphasizes the need to properly track the regime of validity of all approximations.