Response of Uniformly Accelerated Particle Detectors in the Presence of Co-Accelerated Mirrors

We obtain the transition rates for an Unruh-DeWitt particle detector which uniformly accelerates in the presence of a perfectly reflecting spherical mirror that contracts and expands with constant acceleration. We also consider the case when the detector accelerates between two such mirrors, as well as the corresponding reduced configurations in a two dimensional Minkowski space. The mirror and detector accelerations are chosen such that the transition rates are independent of time. In all cases we find that the response respects the detailed balance condition for the Unruh-Davies temperature associated to the detector's acceleration. An interesting fact is that for the detector between the mirrors the transition spectrum in two dimensions is discrete, while in four dimensions it is continuous.