Inversion of statistics and thermalization in the Unruh effect

TL;DR

This paper derives a master equation for an accelerating quantum detector, showing it thermalizes to a Gibbs state, and explores how statistics inversion affects its thermal behavior compared to static detectors in thermal fields.

Contribution

It introduces a general master equation for accelerated detectors in arbitrary dimensions and analyzes the impact of statistics inversion on their thermalization process.

Findings

Detector asymptotically reaches a Gibbs state.

Statistics inversion influences the detector's thermal behavior.

Differences between accelerated and static detectors in thermal fields.

Abstract

We derive a master equation for the reduced density matrix of a uniformly accelerating quantum detector in arbitrary dimensions, generically coupled to a field initially in its vacuum state, and analyze its late time regime. We find that such density matrix asymptotically reaches a Gibbs state. The particularities of its evolution towards this state are encoded in the response function, which depends on the dimension, the properties of the fields, and the specific coupling to them. We also compare this situation with the thermalization of a static detector immersed in a thermal field state, pinpointing the differences between both scenarios. In particular, we analyze the role of the response function and its effect on the evolution of the detector towards equilibrium. Furthermore, we explore the consequences of the well-known statistics inversion of the response function of an Unruh-DeWitt detector linearly coupled to a free scalar field in odd spacetime dimensions. This allows us to specify in which sense accelerated detectors in Minkowski vacuum behave as static detectors in a thermal bath and in which sense they do not.