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Geometry and Material Effects in Casimir Physics-Scattering Theory

  • Sahand Jamal RahiEmail author
  • Thorsten Emig
  • Robert L. Jaffe
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 834)

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, to nonzero temperatures, and to 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. This approach, which combines methods of statistical physics and scattering theory, is well suited to analyze many diverse phenomena. We illustrate its power and versatility by a number of examples, which show how the interplay of geometry and material properties helps to understand and control Casimir forces. We also examine whether electrodynamic Casimir forces can lead to stable levitation. Neglecting permeabilities, we prove that any equilibrium position of objects subject to such forces is unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.

Keywords

Partition Function Partial Wave Casimir Force Casimir Energy Parabolic Cylinder 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The research presented here was conducted together with Noah Graham, Steven G. Johnson, Mehran Kardar, Alejandro W. Rodriguez, Pablo Rodriguez-Lopez, Alexander Shpunt, and Saad Zaheer, whom we thank for their collaboration. This work was supported by the National Science Foundation (NSF) through grant DMR-08-03315 (SJR), by the DFG through grant EM70/3 (TE) and by the U. S. Department of Energy (DOE) under cooperative research agreement #DF-FC02-94ER40818 (RLJ).

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Copyright information

© Springer-Verlag Berlin Heidelberg  2011

Authors and Affiliations

  • Sahand Jamal Rahi
    • 1
    • 4
    Email author
  • Thorsten Emig
    • 2
  • Robert L. Jaffe
    • 3
  1. 1.Department of PhysicsMITCambridgeUSA
  2. 2.Laboratoire de Physique Théorique et Modèles StatistiquesUniversité Paris-SudOrsayFrance
  3. 3.Center for Theoretical PhysicsMITCambridgeUSA
  4. 4.Center for Studies in Physics and BiologyThe Rockefeller UniversityNew YorkUSA

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