Circular acceleration in Minkowski spacetime: thermality versus finite size

Abstract

The Unruh effect predicts that a uniformly linearly accelerated observer with proper acceleration $a$ reacts to the Minkowski vacuum through excitations and de-excitations with the characteristics of a thermal state at temperature $T_U=a/(2π)$. An observer in uniform circular motion will experience similar excitations and de-excitations that we may use to operationally define an effective temperature, which however depends not only on the acceleration but also on the orbital speed and excitation energy. Motivated by the experimental interest in the circular motion Unruh effect, we investigate how spatial confinement modifies the response of an Unruh-DeWitt detector in $2+1$ Minkowski spacetime. We consider a massless scalar field confined within a circular boundary prepared in either the vacuum or a thermal state, probed by an Unruh-DeWitt detector on a circular orbit, a setting that describes proposed analogue spacetime systems for testing the effect, and in which both a boundary and an ambient temperature will necessarily be present. We establish analytic results for the detector response in the large-boundary regime and identify resonance peaks, which are more prominent when the field has an ambient temperature.