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Title: Hamiltonian Approach to the Dynamical Casimir Effect

Abstract

A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term--proportional to the mirrors' acceleration - which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors - while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out.

Authors:
 [1];  [2]
  1. Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain)
  2. Instituto de Ciencias del Espacio (CSIC) and Institut d'Estudis Espacials de Catalunya (IEEC/CSIC), Facultat de Ciencies, Universitat Autonoma de Barcelona, Torre C5-Parell-2a Planta, 08193 Bellaterra Barcelona (Spain)
Publication Date:
OSTI Identifier:
20860867
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 97; Journal Issue: 13; Other Information: DOI: 10.1103/PhysRevLett.97.130401; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCELERATION; CASIMIR EFFECT; COMPARATIVE EVALUATIONS; ENERGY CONSERVATION; HAMILTONIANS; ONE-DIMENSIONAL CALCULATIONS; QUASI PARTICLES; SCALAR FIELDS

Citation Formats

Haro, Jaume, and Elizalde, Emilio. Hamiltonian Approach to the Dynamical Casimir Effect. United States: N. p., 2006. Web. doi:10.1103/PHYSREVLETT.97.130401.
Haro, Jaume, & Elizalde, Emilio. Hamiltonian Approach to the Dynamical Casimir Effect. United States. doi:10.1103/PHYSREVLETT.97.130401.
Haro, Jaume, and Elizalde, Emilio. 2006. "Hamiltonian Approach to the Dynamical Casimir Effect". United States. doi:10.1103/PHYSREVLETT.97.130401.
@article{osti_20860867,
title = {Hamiltonian Approach to the Dynamical Casimir Effect},
author = {Haro, Jaume and Elizalde, Emilio},
abstractNote = {A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term--proportional to the mirrors' acceleration - which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors - while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out.},
doi = {10.1103/PHYSREVLETT.97.130401},
journal = {Physical Review Letters},
number = 13,
volume = 97,
place = {United States},
year = 2006,
month = 9
}
  • Recently [J. Haro and E. Elizalde, Phys. Rev. Lett. 97, 130401 (2006)], a Hamiltonian formulation has been introduced in order to address some long-standing severe problems associated with the physical description of the dynamical Casimir effect at all times while the mirrors are moving. Here we present the complete calculation providing precise details, in particular, of the regularization procedure, which is decisive for the correct derivation of physically meaningful quantities. A basic difference when comparing with the results previously obtained by other authors is the fact that the motion force derived in our approach contains a reactive term--proportional to themore » mirrors' acceleration. This is of the essence in order to obtain particles with a positive energy at all times during the oscillation of the mirrors--while always satisfying the energy conservation law. A careful analysis of the interrelations among the different results previously obtained in the literature is then carried out. For simplicity, the specific case of a neutral scalar field in one dimension, with one or two partially transmitting mirrors (a fundamental proviso for the regularization issue), is considered in more detail, but our general method is shown to be generalizable, without essential problems (Sec. II of this paper), to fields of any kind in two and higher dimensions.« less
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  • The experimental observation of intense light emission by acoustically driven, periodically collapsing bubbles of air in water (sonoluminescence) has yet to receive an adequate explanation. One of the most intriguing ideas is that the conversion of acoustic energy into photons occurs quantum mechanically, through a dynamical version of the Casimir effect. We have argued elsewhere that in the adiabatic approximation, which should be reliable here, Casimir or zero-point energies cannot possibly be large enough to be relevant. (About 10 MeV of energy is released per collapse.) However, there are sufficient subtleties involved that others have come to opposite conclusions. Inmore » particular, it has been suggested that bulk energy, that is, simply the naive sum of (1) /(2) {h_bar}{omega}, which is proportional to the volume, could be relevant. We show that this cannot be the case, based on general principles as well as specific calculations. In the process we further illuminate some of the divergence difficulties that plague Casimir calculations, with an example relevant to the bag model of hadrons. {copyright} {ital 1998} {ital The American Physical Society}« less
  • In this paper we present some calculations regarding the average number of photons produced in the dynamical Casimir effect for the ideal case of two perfectly conducting uncharged parallel plates, using the zero-point energy summation method. We show that it is possible to create intense photon radiation when the two plates are modulated periodically.