Unruh-DeWitt detector event rate for trajectories with time-dependent acceleration

TL;DR

This paper develops an adiabatic expansion method to analyze the response function of an Unruh--DeWitt detector with time-dependent acceleration, revealing how the detector's spectrum evolves with changing acceleration.

Contribution

It introduces an adiabatic expansion approach for the detector response function, accounting for time-dependent acceleration and its derivatives, extending previous static acceleration analyses.

Findings

Recover a Planckian spectrum at lowest order with temperature proportional to instantaneous acceleration.

Higher-order terms involve derivatives of acceleration, affecting the spectral shape.

Application to a trajectory with finite-time acceleration transition demonstrates the method's utility.

Abstract

We analyse the response function of an Unruh--DeWitt detector moving with time-dependent acceleration along a one-dimensional trajectory in Minkowski spacetime. To extract the physics of the process, we propose an adiabatic expansion of this response function. This expansion is also a useful tool for computing the click rate of detectors in general trajectories. The expansion is done in powers of the time derivatives of the acceleration (jerk, snap, and higher derivatives). At the lowest order, we recover a Planckian spectrum with temperature proportional to the acceleration of the detector at each instant of the trajectory. Higher orders in the expansion involve powers of the derivatives of the acceleration, with well-behaved spectral coefficients with different shapes. Finally, we illustrate this analysis in the case of an initially inertial trajectory that acquires a given constant acceleration in a finite time.