Asymptotically thermal responses for smoothly switched detectors

TL;DR

This paper demonstrates that for smoothly switched detectors in quantum field theory, the thermal response characterized by the Unruh temperature emerges asymptotically at large energy gaps when the interaction duration is sufficiently long, highlighting the importance of adiabatic switching.

Contribution

It shows that asymptotic thermal responses occur for smoothly switched detectors at large energy gaps, extending the understanding of thermal phenomena in quantum field theory beyond idealized infinite interaction times.

Findings

Unruh temperature emerges asymptotically for adiabatically switched detectors.

Thermal detailed balance cannot hold exactly for finite-time interactions.

Longer interaction times lead to approximate thermal responses at large energy gaps.

Abstract

Thermal phenomena in quantum field theory can be detected with the aid of particle detectors coupled to quantum fields along stationary worldlines, by testing whether the response of such a detector satisfies the detailed balance version of the KMS condition at a constant temperature. This relation holds when the interaction between the field and the detector has infinite time duration. Operationally, however, detectors interact with fields for a finite amount of time, controlled by a switching function of compact support, and the KMS detailed balance condition cannot hold exactly for finite time interactions at arbitrarily large detector energy gap. In this large energy gap regime, we show that, for an adiabatically switched Rindler detector, the Unruh temperature emerges asymptotically after the detector and the field have interacted for a time that is polynomially long in the large energy. We comment on the significance of the adiabaticity assumption in this result.