Probing non-equilibrium steady states of the Klein-Gordon field with Unruh-DeWitt detectors

TL;DR

This paper investigates how an Unruh-DeWitt detector perceives a non-equilibrium steady state of a scalar field, revealing that it only detects kinematical effects and not the heat flow dynamics.

Contribution

It provides a detailed calculation of the detector's transition rate in a NESS, highlighting the detector's insensitivity to heat flow and the hidden dynamical features.

Findings

Detector only registers kinematical effects, not heat flow.

Modewise thermal properties of the NESS are confirmed.

Dynamical features of the NESS are hidden from the detector.

Abstract

We calculate the transition rate of an Unruh-DeWitt detector coupled to a non-equilibrium steady state (NESS) of a free massless scalar field on four-dimensional Minkowski spacetime. Bringing two semi-infinite heat baths at different temperatures into thermal contact along a surface, the NESS arises at asymptotically late times as a stationary state that has modewise thermal properties and features a heat flow between the reservoirs. The detector couples linearly to the field by a monopole interaction, and it moves inertially along the axis of the NESS heat flow. We contrast the transition rate with the case of a detector that is coupled to an inertial thermal equilibrium state. The results illustrate that the monopole does not couple to the heat flow, causing the detector to only register kinematical effects. Hence dynamical features of the NESS are hidden from this detector model.