Velocity Effects on an Accelerated Unruh-DeWitt Detector

TL;DR

This paper investigates how an Unruh-DeWitt detector's response varies with velocity and acceleration in a two-dimensional space, revealing velocity-dependent effects in different energy regimes compared to thermal bath scenarios.

Contribution

It introduces a detailed analysis of an accelerated detector with rotating acceleration in 2D space, comparing its response to inertial detectors in thermal baths across energy regimes.

Findings

Infrared regime: higher speed needed for the detector to match inertial detector excitation rates.

Ultraviolet regime: response modifications align with those of a detector moving at constant velocity in a thermal bath.

Response depends on both acceleration and velocity, affecting the perceived Unruh radiation spectrum.

Abstract

We analyze the response of an Unruh-DeWitt detector moving along an unbounded spatial trajectory in a two-dimensional spatial plane with constant independent magnitudes of both the four-acceleration and of a timelike proper time derivative of the four-accelration. In a Fermi-Walker frame moving with the detector, the direction of the acceleration rotates at a constant rate around a great circle. This is the motion of a charge in a uniform electric field when in the frame of the charge there is both an electric and a magnetic field. We compare the response of this detector to a detector moving with constant velocity in a thermal bath of the corresponding temperature for non-relativistic velocities, and in two regimes: ultraviolet and infrared. In infrared regime, the detector in the Minkowski space-time moving along the spatially two-dimensional trajectory should move with a higher speed to keep up with the same excitation rate of the inertial detector in a thermal bath. In ultraviolet regime, the dominant modification in the response of this detector compared to the black body spectrum of Unruh radiation is the same as the dominant modification perceived by a detector moving with constant velocity in a thermal bath.