Reliable quantum master equation of the Unruh-DeWitt detector

TL;DR

This paper develops criteria to determine when the quantum Markovian master equation reliably describes the Unruh-DeWitt detector's dynamics, especially in the context of the Unruh effect, without requiring exact solutions.

Contribution

It introduces a relaxed van Hove limit and provides a perturbative error estimate to assess the validity of the Markovian approximation in open quantum systems.

Findings

Reliability criteria for the Markov approximation

Conditions for the rotating wave approximation validity

Application to an accelerating detector under the Unruh effect

Abstract

In this paper, we present a method for estimating the validity range of the quantum Markovian master equation as applied to the Unruh-DeWitt (UDW) detector within a broader context, particularly without necessitating an exact solution for the detector's evolution. We propose a relaxed van Hove limit (i.e., late-time limit) and offer a perturbative estimate of the error order resulting from the standard derivation procedure of open quantum dynamics. Our primary findings include reliability criteria for the Markov approximation and conditions for the applicability of the rotating wave approximation. Nevertheless, the specific forms of these validity conditions rely on the details of the detector-field system, such as the spacetime background, the trajectory of the detector, and the type of quantum field being analyzed. Finally, we illustrate our results by reexamining the open dynamics of an accelerating UDW detector undergoing the Unruh effect, where the validity conditions narrow the parameter space to ensure the solution's reliability regarding the quantum Markovian master equation.