Timeofarrival probabilities and quantum measurements
Abstract
In this paper we study the construction of probability densities for time of arrival in quantum mechanics. Our treatment is based upon the facts that (i) time appears in quantum theory as an external parameter to the system, and (ii) propositions about the time of arrival appear naturally when one considers histories. The definition of timeofarrival probabilities is straightforward in stochastic processes. The difficulties that arise in quantum theory are due to the fact that the time parameter of the Schroedinger's equation does not naturally define a probability density at the continuum limit, but also because the procedure one follows is sensitive on the interpretation of the reduction procedure. We consider the issue in Copenhagen quantum mechanics and in historybased schemes like consistent histories. The benefit of the latter is that it allows a proper passage to the continuous limitthere are, however, problems related to the quantum Zeno effect and decoherence. We finally employ the historiesbased description to construct PositiveOperatorValuedMeasures (POVMs) for the timeofarrival, which are valid for a general Hamiltonian. These POVMs typically depend on the resolution of the measurement device; for a free particle, however, this dependence cancels in the physically relevant regime and the POVM coincides withmore »
 Authors:
 Department of Physics, University of Patras, 26500 Patras (Greece)
 (United Kingdom)
 Publication Date:
 OSTI Identifier:
 20861552
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 12; Other Information: DOI: 10.1063/1.2399085; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HAMILTONIANS; PROBABILITY; QUANTUM MECHANICS; SCHROEDINGER EQUATION; STOCHASTIC PROCESSES
Citation Formats
Anastopoulos, Charis, Savvidou, Ntina, and Theoretical Physics Group, Imperial College, SW7 2BZ, London. Timeofarrival probabilities and quantum measurements. United States: N. p., 2006.
Web. doi:10.1063/1.2399085.
Anastopoulos, Charis, Savvidou, Ntina, & Theoretical Physics Group, Imperial College, SW7 2BZ, London. Timeofarrival probabilities and quantum measurements. United States. doi:10.1063/1.2399085.
Anastopoulos, Charis, Savvidou, Ntina, and Theoretical Physics Group, Imperial College, SW7 2BZ, London. Fri .
"Timeofarrival probabilities and quantum measurements". United States.
doi:10.1063/1.2399085.
@article{osti_20861552,
title = {Timeofarrival probabilities and quantum measurements},
author = {Anastopoulos, Charis and Savvidou, Ntina and Theoretical Physics Group, Imperial College, SW7 2BZ, London},
abstractNote = {In this paper we study the construction of probability densities for time of arrival in quantum mechanics. Our treatment is based upon the facts that (i) time appears in quantum theory as an external parameter to the system, and (ii) propositions about the time of arrival appear naturally when one considers histories. The definition of timeofarrival probabilities is straightforward in stochastic processes. The difficulties that arise in quantum theory are due to the fact that the time parameter of the Schroedinger's equation does not naturally define a probability density at the continuum limit, but also because the procedure one follows is sensitive on the interpretation of the reduction procedure. We consider the issue in Copenhagen quantum mechanics and in historybased schemes like consistent histories. The benefit of the latter is that it allows a proper passage to the continuous limitthere are, however, problems related to the quantum Zeno effect and decoherence. We finally employ the historiesbased description to construct PositiveOperatorValuedMeasures (POVMs) for the timeofarrival, which are valid for a general Hamiltonian. These POVMs typically depend on the resolution of the measurement device; for a free particle, however, this dependence cancels in the physically relevant regime and the POVM coincides with that of Kijowski.},
doi = {10.1063/1.2399085},
journal = {Journal of Mathematical Physics},
number = 12,
volume = 47,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}

Contributed Review: Sourcelocalization algorithms and applications using time of arrival and time difference of arrival measurements
Locating the position of fixed or mobile sources (i.e., transmitters) based on received measurements from sensors is an important research area that is attracting much research interest. In this paper, we present localization algorithms using time of arrivals (TOA) and time difference of arrivals (TDOA) to achieve high accuracy under lineofsight conditions. The circular (TOA) and hyperbolic (TDOA) location systems both use nonlinear equations that relate the locations of the sensors and tracked objects. These nonlinear equations can develop accuracy challenges because of the existence of measurement errors and efficiency challenges that lead to high computational burdens. Least squaresbased andmore »