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Title: Quantum arrival and dwell times via idealized clocks

Abstract

A number of approaches to the problem of defining arrival- and dwell-time probabilities in quantum theory makes use of idealized models of clocks. An interesting question is the extent to which the probabilities obtained in this way are related to standard semiclassical results. In this paper, we explore this question using a reasonably general clock model, solved using path-integral methods. We find that, in the weak-coupling regime, where the energy of the clock is much less than the energy of the particle it is measuring, the probability for the clock pointer can be expressed in terms of the probability current in the case of arrival times, and the dwell-time operator in the case of dwell times, the expected semiclassical results. In the regime of strong system-clock coupling, we find that the arrival-time probability is proportional to the kinetic-energy density, consistent with an earlier model involving a complex potential. We argue that, properly normalized, this may be the generically expected result in this regime. We show that these conclusions are largely independent of the form of the clock Hamiltonian.

Authors:
; ; ;  [1]
  1. Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)
Publication Date:
OSTI Identifier:
22068487
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 2; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; COUPLING; HAMILTONIANS; KINETIC ENERGY; PATH INTEGRALS; PROBABILITY; SEMICLASSICAL APPROXIMATION

Citation Formats

Yearsley, J M, Downs, D A, Halliwell, J J, and Hashagen, A K. Quantum arrival and dwell times via idealized clocks. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.022109.
Yearsley, J M, Downs, D A, Halliwell, J J, & Hashagen, A K. Quantum arrival and dwell times via idealized clocks. United States. https://doi.org/10.1103/PHYSREVA.84.022109
Yearsley, J M, Downs, D A, Halliwell, J J, and Hashagen, A K. 2011. "Quantum arrival and dwell times via idealized clocks". United States. https://doi.org/10.1103/PHYSREVA.84.022109.
@article{osti_22068487,
title = {Quantum arrival and dwell times via idealized clocks},
author = {Yearsley, J M and Downs, D A and Halliwell, J J and Hashagen, A K},
abstractNote = {A number of approaches to the problem of defining arrival- and dwell-time probabilities in quantum theory makes use of idealized models of clocks. An interesting question is the extent to which the probabilities obtained in this way are related to standard semiclassical results. In this paper, we explore this question using a reasonably general clock model, solved using path-integral methods. We find that, in the weak-coupling regime, where the energy of the clock is much less than the energy of the particle it is measuring, the probability for the clock pointer can be expressed in terms of the probability current in the case of arrival times, and the dwell-time operator in the case of dwell times, the expected semiclassical results. In the regime of strong system-clock coupling, we find that the arrival-time probability is proportional to the kinetic-energy density, consistent with an earlier model involving a complex potential. We argue that, properly normalized, this may be the generically expected result in this regime. We show that these conclusions are largely independent of the form of the clock Hamiltonian.},
doi = {10.1103/PHYSREVA.84.022109},
url = {https://www.osti.gov/biblio/22068487}, journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 84,
place = {United States},
year = {Mon Aug 15 00:00:00 EDT 2011},
month = {Mon Aug 15 00:00:00 EDT 2011}
}