The role of diffraction in the Casimir effect beyond the proximity force approximation

We derive the leading-order correction to the proximity force approximation (PFA) result for the electromagnetic Casimir interaction in the plane-sphere geometry by developing the scattering approach in the plane-wave basis. Expressing the Casimir energy as a sum over round trips between plane and s...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Henning, Vinicius, Spreng, Benjamin, Hartmann, Michael, Gert-Ludwig Ingold, Maia Neto, Paulo A
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.11.2018
Subjects
Approximation
Diffraction
Mathematical analysis
Mie scattering
Physics - Quantum Physics
Scattering amplitude
Specular reflection
Yang-Mills theory
Online AccessGet full text

Cover

More Information
Summary:We derive the leading-order correction to the proximity force approximation (PFA) result for the electromagnetic Casimir interaction in the plane-sphere geometry by developing the scattering approach in the plane-wave basis. Expressing the Casimir energy as a sum over round trips between plane and sphere, we find two distinct contributions to the correction. The first one results from the variation of the Mie reflection operator, calculated within the geometric optical WKB approximation, over the narrow Fourier interval associated to specular reflection at the vicinity of the point of closest approach on the spherical surface. The second contribution, accounting for roughly 90% of the total correction, results from the modification of the geometric optical WKB Mie scattering amplitude due to diffraction. Our derivation provides a clear physical understanding of the nature of the PFA correction for spherical surfaces.
ISSN:2331-8422
DOI:10.48550/arxiv.1811.12856