Thermality and athermality in the Unruh effect

TL;DR

The paper analyzes an Unruh–DeWitt detector with finite mass to examine how center-of-mass (CoM) motion interacts with the Unruh bath. Using a co-moving (Rindler) frame and an inertial-frame perspective, it shows that the CoM does not satisfy the KMS condition and hence does not fully thermalize with the Unruh bath, while the internal energy levels do thermalize at the Unruh temperature $T_U = a/(2\pi)$. The fluctuation-dissipation theorem holds for internal DOF, with CoM effects appearing as mass-dependent shifts in the energy gap but not destroying internal thermalization. These results clarify which detector observables can test Unruh thermality and highlight the role of recoil in acceleration-induced thermalization.

Abstract

In idealized treatments of the Unruh effect, a two-level atom is accelerated in a prescribed classical trajectory through the vacuum of a quantum field -- the Unruh bath -- which causes the atom's internal state to thermalize to a temperature proportional to the acceleration. This happens via emission and absorption of quanta by the atom, leading to a detailed balance between fluctuations in the Unruh bath and associated dissipation of the atom's internal energy. In any physical manifestation of the Unruh effect, the center-of-mass (CoM) degree of freedom of the atom is dynamical, and is therefore coupled to the Unruh bath via momentum recoil during the absorption/emission process. We study this scenario and show how the fluctuation-dissipation theorem fails for the CoM degree of freedom, while still being upheld for the internal energy. That is, the CoM of an accelerated atom is not in thermal equilibrium with the Unruh bath, while its internal level can be.