Scattering theory approach to electrodynamic Casimir forces

By S. Rahi, Thorsten Emig, N. Graham, R. Jaffe, Mehran Kardar. 2009

212 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Civil and Structural Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1685375c88f187e471a3cd4bb72959fd65701cb0

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In Atomic and Molecular Physics, and Optics

In Civil and Structural Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Materials perspective on Casimir and van der Waals interactions (2015, methodology): “The interaction energy can written in the form (Lambrecht et al., 2006; Lambrecht and Marachevsky, 2008; Rahi et al., 2009) E(C) = −~ ∫ dω 2π ∫ dk‖ 2π2 ln Det[I− R1(iω)R2(iω)e−2d √ ω2 c2 +k2‖ ], (9) where R1,2 are the reflection matrices of the individual objects evaluated at imaginary frequencies.”