Waiting for Unruh

Fewster, Christopher J.; Ju�rez-Aubry, Benito A.; Louko, Jorma

Abstract

How long does a uniformly accelerated observer need to interact with a quantum field in order to record thermality in the Unruh temperature? We address this question for a pointlike Unruh–DeWitt detector, coupled linearly to a real Klein–Gordon field of mass and treated within first order perturbation theory, in the limit of large detector energy gap . We first show that when the interaction duration is fixed, thermality in the sense of detailed balance cannot hold as , and this property generalises from the Unruh effect to any Kubo–Martin–Schwinger state satisfying certain technical conditions. We then specialise to a massless field in four spacetime dimensions and show that detailed balance does hold when grows as a power-law in as , provided the switch-on and switch-off intervals are stretched proportionally to and the switching function has sufficiently strong Fourier decay. By contrast, if grows by stretching a plateau in which the interaction remains at constant strength but keeping the duration of the switch-on and switch-off intervals fixed, detailed balance at requires to grow faster than any polynomial in , under mild technical conditions. The results also hold for a static detector in a Minkowski heat bath. The results limit the utility of the large regime as a probe of thermality in time-dependent versions of the Hawking and Unruh effects, such as an observer falling into a radiating black hole. They may also have implications on the design of prospective experimental tests of the Unruh effect.

Citation

Fewster, C. J., Juárez-Aubry, B. A., & Louko, J. (2016). Waiting for Unruh. Classical and Quantum Gravity, 33(16), Article 165003. https://doi.org/10.1088/0264-9381/33/16/165003

• Journal Article Type: Article
• Acceptance Date: Jun 24, 2016
• Online Publication Date: Jul 18, 2016
• Publication Date: Aug 18, 2016
• Deposit Date: Jul 7, 2017
• Publicly Available Date: Jul 7, 2017
• Journal: Classical and Quantum Gravity
• Print ISSN: 0264-9381
• Electronic ISSN: 1361-6382
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 16
• Article Number: 165003
• DOI: https://doi.org/10.1088/0264-9381/33/16/165003
• Keywords: Unruh effect, Unruh–DeWitt detector, Approach to detailed balance
• Public URL: https://nottingham-repository.worktribe.com/output/800565
• Publisher URL: https://doi.org/10.1088/0264-9381/33/16/165003
• Related Public URLs: http://eprints.whiterose.ac.uk/102725/; https://arxiv.org/abs/1605.01316
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication in Classical and Quantum Gravity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/0264-9381/33/16/165003
• Contract Date: Jul 7, 2017