Nonperturbative approach to Casimir interactions in periodic geometries

Journal Article · Tue Jun 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.69.062101· OSTI ID:20643715

Buescher, Rauno; Emig, Thorsten ^[1]

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1. Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse 77, 50937 Cologne (Germany)

Due to their collective nature Casimir forces can strongly depend on the geometrical shape of the interacting objects. We study the effect of strong periodic shape deformations of two ideal metal plates on their quantum interaction. A nonperturbative approach which is based on a path-integral quantization of the electromagnetic field is presented in detail. Using this approach, we compute the force for the specific case of a flat plate and a plate with a rectangular corrugation. We obtain complementary analytical and numerical results which allow us to identify two different scaling regimes for the force as a function of the mean plate distance, corrugation amplitude, and wavelength. Qualitative distinctions between transversal electric and magnetic modes are revealed. Our results demonstrate the importance of a careful consideration of the nonadditivity of Casimir forces, especially in strongly nonplanar geometries. Nonperturbative effects due to surface edges are found. Strong deviations from the commonly used proximity force approximation emerge over a wide range of corrugation wavelengths, even though the surface is composed only of flat segments. We compare our results to that of a perturbative approach and a classical optics approximation.

• OSTI ID: 20643715
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 69; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
AMPLITUDES
BASIC INTERACTIONS
CASIMIR EFFECT
COMPARATIVE EVALUATIONS
DEFORMATION
DISTANCE
ELECTROMAGNETIC FIELDS
GEOMETRY
METALS
OPTICS
PATH INTEGRALS
PERIODICITY
PLATES
QUANTIZATION
QUANTUM ELECTRODYNAMICS
SHAPE
SURFACES
WAVELENGTHS