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Title: Scattering theory approach to electrodynamic Casimir forces

Abstract

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by rederiving the Lifshitz formula for infinite half-spaces, by demonstrating the Casimir-Polder to van der Waals crossover, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely, the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

Authors:
;  [1];  [1];  [2];  [1]
  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
  2. Department of Physics, Middlebury College, Middlebury, Vermont 05753 (United States)
Publication Date:
OSTI Identifier:
21325411
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 80; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.80.085021; (c) 2009 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:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; CASIMIR EFFECT; CYLINDERS; INTERACTIONS; PERMEABILITY; PERMITTIVITY; SCATTERING; SCATTERING AMPLITUDES; VAN DER WAALS FORCES

Citation Formats

Rahi, Sahand Jamal, Kardar, Mehran, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, Emig, Thorsten, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Koeln, Laboratoire de Physique Theorique et Modeles Statistiques, CNRS UMR 8626, Universite Paris-Sud, 91405 Orsay cedex, Graham, Noah, Jaffe, Robert L, and Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Scattering theory approach to electrodynamic Casimir forces. United States: N. p., 2009. Web. doi:10.1103/PHYSREVD.80.085021.
Rahi, Sahand Jamal, Kardar, Mehran, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, Emig, Thorsten, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Koeln, Laboratoire de Physique Theorique et Modeles Statistiques, CNRS UMR 8626, Universite Paris-Sud, 91405 Orsay cedex, Graham, Noah, Jaffe, Robert L, & Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Scattering theory approach to electrodynamic Casimir forces. United States. https://doi.org/10.1103/PHYSREVD.80.085021
Rahi, Sahand Jamal, Kardar, Mehran, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, Emig, Thorsten, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Koeln, Laboratoire de Physique Theorique et Modeles Statistiques, CNRS UMR 8626, Universite Paris-Sud, 91405 Orsay cedex, Graham, Noah, Jaffe, Robert L, and Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. 2009. "Scattering theory approach to electrodynamic Casimir forces". United States. https://doi.org/10.1103/PHYSREVD.80.085021.
@article{osti_21325411,
title = {Scattering theory approach to electrodynamic Casimir forces},
author = {Rahi, Sahand Jamal and Kardar, Mehran and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106 and Emig, Thorsten and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106 and Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Koeln and Laboratoire de Physique Theorique et Modeles Statistiques, CNRS UMR 8626, Universite Paris-Sud, 91405 Orsay cedex and Graham, Noah and Jaffe, Robert L and Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139},
abstractNote = {We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by rederiving the Lifshitz formula for infinite half-spaces, by demonstrating the Casimir-Polder to van der Waals crossover, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely, the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.},
doi = {10.1103/PHYSREVD.80.085021},
url = {https://www.osti.gov/biblio/21325411}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 80,
place = {United States},
year = {2009},
month = {10}
}