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Title: Unruh effect for general trajectories

Abstract

We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the Feynman prescription that is explicitly causal, and we compare it to other expressions used in the literature. We then use this expression to study, analytically and numerically, the time dependence of the response function in various nonstationarity situations. We show that, generically, the response function decreases like a power in the detector's level spacing, E, for high E. It is only for stationary worldlines that the response function decays faster than any power law, in keeping with the known exponential behavior for some stationary cases. Under some conditions the (time-dependent) response function for a nonstationary worldline is well approximated by the value of the response function for a stationary worldline having the same instantaneous acceleration, torsion, and hypertorsion. While we cannot offer general conditions for this to apply, we discuss special cases; in particular, the low-energy limit for linear space trajectories.

Authors:
;  [1]
  1. Center for Astrophysics, Weizmann Institute of Science, Rehovot (Israel)
Publication Date:
OSTI Identifier:
21020185
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.065006; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACCELERATION; BLACK HOLES; COMPARATIVE EVALUATIONS; COSMOLOGY; FEYNMAN DIAGRAM; MINKOWSKI SPACE; QUANTUM FIELD THEORY; RESPONSE FUNCTIONS; SCALAR FIELDS; SPACE-TIME; TIME DEPENDENCE; TORSION

Citation Formats

Obadia, N, and Milgrom, M. Unruh effect for general trajectories. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.065006.
Obadia, N, & Milgrom, M. Unruh effect for general trajectories. United States. https://doi.org/10.1103/PHYSREVD.75.065006
Obadia, N, and Milgrom, M. 2007. "Unruh effect for general trajectories". United States. https://doi.org/10.1103/PHYSREVD.75.065006.
@article{osti_21020185,
title = {Unruh effect for general trajectories},
author = {Obadia, N and Milgrom, M},
abstractNote = {We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the Feynman prescription that is explicitly causal, and we compare it to other expressions used in the literature. We then use this expression to study, analytically and numerically, the time dependence of the response function in various nonstationarity situations. We show that, generically, the response function decreases like a power in the detector's level spacing, E, for high E. It is only for stationary worldlines that the response function decays faster than any power law, in keeping with the known exponential behavior for some stationary cases. Under some conditions the (time-dependent) response function for a nonstationary worldline is well approximated by the value of the response function for a stationary worldline having the same instantaneous acceleration, torsion, and hypertorsion. While we cannot offer general conditions for this to apply, we discuss special cases; in particular, the low-energy limit for linear space trajectories.},
doi = {10.1103/PHYSREVD.75.065006},
url = {https://www.osti.gov/biblio/21020185}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}