Unruh and analogue Unruh temperatures for circular motion in 3+1 and 2+1 dimensions

Biermann, Steffen; Erne, Sebastian; Gooding, Cisco; Louko, Jorma; Schmiedmayer, J�rg; Unruh, William G.; Weinfurtner, Silke

Abstract

The Unruh effect states that a uniformly linearly accelerated observer with proper acceleration a experiences Minkowski vacuum as a thermal state in the temperature Tlin=a/(2?), operationally measurable via the detailed balance condition between excitation and deexcitation probabilities. An observer in uniform circular motion experiences a similar Unruh-type temperature Tcirc, operationally measurable via the detailed balance condition, but Tcirc depends not just on the proper acceleration but also on the orbital radius and on the excitation energy. We establish analytic results for Tcirc for a massless scalar field in 3+1 and 2+1 spacetime dimensions in several asymptotic regions of the parameter space, and we give numerical results in the interpolating regions. In the ultrarelativistic limit, we verify that in 3+1 dimensions Tcirc is of the order of Tlin uniformly in the energy, as previously found by Unruh, but in 2+1 dimensions, Tcirc is significantly lower at low energies. We translate these results to an analogue spacetime nonrelativistic field theory in which the circular acceleration effects may become experimentally testable in the near future. We establish in particular that the circular motion analogue Unruh temperature grows arbitrarily large in the near-sonic limit, encouragingly for the experimental prospects, but the growth is weaker in effective spacetime dimension 2+1 than in 3+1.

Citation

Biermann, S., Erne, S., Gooding, C., Louko, J., Schmiedmayer, J., Unruh, W. G., & Weinfurtner, S. (2020). Unruh and analogue Unruh temperatures for circular motion in 3+1 and 2+1 dimensions. Physical Review D, 102(8), Article 085006. https://doi.org/10.1103/PhysRevD.102.085006

• Journal Article Type: Article
• Acceptance Date: Sep 21, 2020
• Online Publication Date: Oct 13, 2020
• Publication Date: Oct 13, 2020
• Deposit Date: Oct 15, 2020
• Publicly Available Date: Oct 15, 2020
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 102
• Issue: 8
• Article Number: 085006
• DOI: https://doi.org/10.1103/PhysRevD.102.085006
• Keywords: Physics and Astronomy (miscellaneous)
• Public URL: https://nottingham-repository.worktribe.com/output/4966652
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.102.085006