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Title: Quantum radiation force on the moving mirror of a cavity, with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state

Abstract

We consider a real massless scalar field inside a cavity with a moving mirror in a two-dimensional spacetime, satisfying the Dirichlet or Neumann boundary condition at the instantaneous position of the boundaries, for an arbitrary and relativistic law of motion. Considering an arbitrary initial field state, we show that the exact value of the energy density in the cavity can be obtained by tracing back a sequence of null lines, connecting the value of the energy density at the given spacetime point to a certain known value of the energy density at a point in the region where the initial field modes are not affected by the boundary motion. We obtain the particular formulas for the energy density of the field and the quantum force acting on the boundaries for a vacuum, thermal, and a coherent state. We thus generalize a previous result in literature, where this problem is approached for only one mirror. For the particular cases of vacuum and Dirichlet boundary condition, nonrelativistic velocities, or in the limit of large length of the cavity, our results coincide with those found in the literature.

Authors:
; ;  [1];  [2]
  1. Faculdade de Fisica, Universidade Federal do Para, 66075-110, Belem, PA (Brazil)
  2. Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ (Brazil)
Publication Date:
OSTI Identifier:
21409118
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 81; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.81.025016; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; BOUNDARY CONDITIONS; CAVITIES; DIRICHLET PROBLEM; EIGENSTATES; ENERGY DENSITY; RELATIVISTIC RANGE; SCALAR FIELDS; SPACE-TIME; TWO-DIMENSIONAL CALCULATIONS; VELOCITY; BOUNDARY-VALUE PROBLEMS; ENERGY RANGE; MATHEMATICAL OPERATORS; QUANTUM OPERATORS

Citation Formats

Alves, Danilo T, Silva, Hector O, Lima, Mateus G, and Granhen, Edney R. Quantum radiation force on the moving mirror of a cavity, with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.81.025016.
Alves, Danilo T, Silva, Hector O, Lima, Mateus G, & Granhen, Edney R. Quantum radiation force on the moving mirror of a cavity, with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state. United States. https://doi.org/10.1103/PHYSREVD.81.025016
Alves, Danilo T, Silva, Hector O, Lima, Mateus G, and Granhen, Edney R. 2010. "Quantum radiation force on the moving mirror of a cavity, with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state". United States. https://doi.org/10.1103/PHYSREVD.81.025016.
@article{osti_21409118,
title = {Quantum radiation force on the moving mirror of a cavity, with Dirichlet and Neumann boundary conditions for a vacuum, finite temperature, and a coherent state},
author = {Alves, Danilo T and Silva, Hector O and Lima, Mateus G and Granhen, Edney R},
abstractNote = {We consider a real massless scalar field inside a cavity with a moving mirror in a two-dimensional spacetime, satisfying the Dirichlet or Neumann boundary condition at the instantaneous position of the boundaries, for an arbitrary and relativistic law of motion. Considering an arbitrary initial field state, we show that the exact value of the energy density in the cavity can be obtained by tracing back a sequence of null lines, connecting the value of the energy density at the given spacetime point to a certain known value of the energy density at a point in the region where the initial field modes are not affected by the boundary motion. We obtain the particular formulas for the energy density of the field and the quantum force acting on the boundaries for a vacuum, thermal, and a coherent state. We thus generalize a previous result in literature, where this problem is approached for only one mirror. For the particular cases of vacuum and Dirichlet boundary condition, nonrelativistic velocities, or in the limit of large length of the cavity, our results coincide with those found in the literature.},
doi = {10.1103/PHYSREVD.81.025016},
url = {https://www.osti.gov/biblio/21409118}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 2,
volume = 81,
place = {United States},
year = {Fri Jan 15 00:00:00 EST 2010},
month = {Fri Jan 15 00:00:00 EST 2010}
}