Inversion of statistics and thermalization in the Unruh effect

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. © 2021 American Physical Society.Financial support was provided by the Spanish Government through the projects FIS2017-86497-C2-1-P, FIS2017-86497-C2-2-P (with FEDER contribution), FIS2016-78859-P (AEI/FEDER, UE), and by the Junta de Andalucia through the project FQM219. Authors J. A., C. B. and G. G. M. acknowledge financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofisica de Andalucia (SEV-2017-0709). G. G. M. acknowledges financial support from Instituto de Fisica de Particulas y del Cosmos through "Ayudas para cursar estudios de Doctorado del Instituto de Fisica de Particulas y del Cosmos."Peer reviewe