Unruh-like effects: effective temperatures along stationary worldlines
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Springer
Received: April 21, 2020 Accepted: May 18, 2020 Published: June 9, 2020
Unruh-like effects: effective temperatures along stationary worldlines
a
Department of Physics, Nazarbayev University, Nur-Sultan 010000, Kazakhstan b Departmento de F´ısica Matem´ atica, Instituto de Investigaciones en Matem´ aticas Aplicadas y en Sistemas, Universidad Nacional Aut´ onoma de M´exico, Mexico City 20126, Mexico c Department of Physics, University of Patras, Patras 26504, Greece
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We study the detailed balance temperatures recorded along all classes of stationary, uniformly accelerated worldlines in four-dimensional Minkowski spacetime, namely along (i) linear uniform acceleration, (ii) cusped, (iii) circular, (iv) catenary, and (v) helix worldlines, among which the Unruh temperature is the particular case for linear uniform acceleration. As a measuring device, we employ an Unruh-DeWitt detector, modeled as a qubit that interacts for a long time with a massless Klein-Gordon field in the vacuum state. The temperatures in each case (i) - (v) are functions of up to three invariant quantities: curvature or proper acceleration, κ, torsion, b, and hypertorsion, ν, and except for the case (i), they depend on the transition frequency difference of the detector, ω. We investigate numerically the behavior of the frequency-dependent temperatures for different values of κ, b, and ν along the stationary worldlines (ii) - (v) and evaluate analytically the regimes where the temperatures recorded along the different worldlines coincide with each other in terms of relevant asymptotic limits for κ, b, or ν, and discuss their physical meaning. We demonstrate that the temperatures in cases (ii) - (v) dip under the Unruh temperature at low frequencies and go above the Unruh temperature for large |ω|. It is our hope that this study will be relevant to the design of experiments seeking to verify the Unruh effect or generalizations thereof. Keywords: Field Theories in Lower Dimensions, Thermal Field Theory ArXiv ePrint: 2004.08225 With gratitude to all essential workers during the COVID-19 pandemic.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)059
JHEP06(2020)059
Michael Good,a Benito A. Ju´ arez-Aubry,b Dimitris Moustosc and Maksat Temirkhana
Contents 1 Introduction
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2 Thermalization of stationary detectors
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effective temperatures Nulltor (linear) worldline Parator (cusped) worldline Ultrator (circular) worldline Infrator (catenary) worldline Hypertor (helix) worldline
7 7 7 10 12 13
4 Conclusions
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A Asymptotic analysis in section 3.3
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B Asymptotic analysis in section 3.4
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C Asymptotic analysis of section 3.5
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1
Introduction
Linearly uniformly accelerated observers in Minkowski spacetime perceive the Minkowski vacuum state as a thermal state at a temperature proportional to their acceleration, known as the Unruh temperature. The Unruh effect [1–3]
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