Thermality and athermality in the Unruh effect

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.