Scattering Theory Approach to Electrodynamic Casimir Forces

Sahand Jamal Rahi 1, 2, Thorsten Emig 1, 2, 3, 4, Noah Graham 5, Robert L. Jaffe 1, 6, Mehran Kardar 1, 7

Physical Review D 80 (2009) 085021

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 re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, 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.

  • 1. Department of Physics,
    Massachusetts Institute of Technology
  • 2. Kavli Institute for Theoretical Physics,
    University of California, Santa Barbara
  • 3. Institut für Theoretische Physik,
    Universität zu Köln
  • 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 5. Middlebury College,
    Middlebury Colleg
  • 6. Department of Physics, Center for Theoretical Physics,
    Massachussetts Institute of Technology (MIT)
  • 7. Kavli Institute for Theoretical Institute,
    University of California, Santa Barbara