General features of the thermalization of particle detectors and the Unruh effect

TL;DR

This paper demonstrates that particle detectors coupled to quantum fields in curved spacetime thermalize to the expected temperature if the field state satisfies the KMS condition, confirming the robustness of the Unruh effect across various operators and detector configurations.

Contribution

It provides a general formalism showing that smeared particle detectors thermalize to the KMS temperature, including the Unruh temperature, regardless of the specific operator coupled to.

Findings

Detectors thermalize to the KMS temperature under certain conditions.

The Unruh effect is robust for arbitrary smeared detectors and operators.

Bounds on system size relate to proper acceleration and curvature.

Abstract

We study the thermalization of smeared particle detectors that couple locally to $any$ operator in a quantum field theory in curved spacetimes. We show that if the field state satisfies the KMS condition with inverse temperature $\beta$ with respect to the detector's local notion of time evolution, reasonable assumptions ensure that the probe thermalizes to the temperature $1/\beta$ in the limit of long interaction times. Our method also imposes bounds on the size of the system with respect to its proper acceleration and spacetime curvature in order to accurately probe the KMS temperature of the field. We then apply this formalism to a uniformly accelerated detector probing the Minkowski vacuum of any CPT symmetric quantum field theory, and show that the detector thermalizes to the Unruh temperature, independently of the operator it couples to. This exemplifies yet again the robustness of the Unruh effect, even when arbitrary smeared detectors are used to probe general operators in a quantum field theory.