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Title: Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation

Abstract

We consider the interaction of a cylindrical graphene sheet with a dielectric half space and with a flat graphene sheet by a generalization of the method of functional determinants. We confirm the proximity force approximation (PFA) for these configurations and calculate the first correction beyond PFA. This can be considered as a generalization of the Lifshitz formula to such configurations.

Authors:
 [1]
  1. University of Leipzig, Institute for Theoretical Physics Vor dem Hospitaltore 1, 04103 Leipzig (Germany)
Publication Date:
OSTI Identifier:
21020182
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.065003; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; APPROXIMATIONS; CORRECTIONS; DIELECTRIC MATERIALS; PLASMA SHEET; PROXIMITY EFFECT; QUANTUM FIELD THEORY; SPACE

Citation Formats

Bordag, M. Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.065003.
Bordag, M. Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation. United States. doi:10.1103/PHYSREVD.75.065003.
Bordag, M. Thu . "Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation". United States. doi:10.1103/PHYSREVD.75.065003.
@article{osti_21020182,
title = {Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation},
author = {Bordag, M.},
abstractNote = {We consider the interaction of a cylindrical graphene sheet with a dielectric half space and with a flat graphene sheet by a generalization of the method of functional determinants. We confirm the proximity force approximation (PFA) for these configurations and calculate the first correction beyond PFA. This can be considered as a generalization of the Lifshitz formula to such configurations.},
doi = {10.1103/PHYSREVD.75.065003},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying the conductor boundary condition, at small separation. For the separation becoming small we derive the first next-to-leading order of the asymptotic expansion in the separation-to-radius ratio {epsilon}. This correction is of order {epsilon}. Opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, {epsilon}ln{epsilon} and {epsilon}(ln{epsilon}){sup 2}. We compare this result with the available findings of numerical and experimental approaches.
  • We argue that the appropriate variable to study a nontrivial geometry dependence of the Casimir force is the lateral component of the Casimir force, which we evaluate between two corrugated metallic plates outside the validity of the proximity-force approximation. The metallic plates are described by the plasma model, with arbitrary values for the plasma wavelength, the plate separation, and the corrugation period, the corrugation amplitude remaining the smallest length scale. Our analysis shows that in realistic experimental situations the proximity-force approximation overestimates the force by up to 30%.
  • The analysis of all Casimir force experiments using a sphere-plate geometry requires the use of the proximity-force approximation (PFA) to relate the Casimir force between a sphere and a flat plate to the Casimir energy between two parallel plates. Because it has been difficult to assess the PFA's range of applicability theoretically, we have conducted an experimental search for corrections to the PFA by measuring the Casimir force and force gradient between a gold-coated plate and five gold-coated spheres with different radii using a microelectromechanical torsion oscillator. For separations z<300 nm, we find that the magnitude of the fractional deviationmore » from the PFA in the force gradient measurement is, at the 95% confidence level, less than 0.4z/R, where R is the radius of the sphere.« less
  • The lateral Casimir force between two corrugated metallic plates makes possible a study of the nontrivial interplay of geometry and Casimir effect appearing beyond the regime of validity of the proximity-force approximation. Quantitative evaluations can be obtained by using scattering theory in a perturbative expansion valid when the corrugation amplitudes are smaller than the three other length scales: the mean separation distance L of the plates, the corrugation period {lambda}{sub C}, and the plasma wavelength {lambda}{sub P}. Within this perturbative expansion, evaluations are obtained for arbitrary relative values of L, {lambda}{sub C}, and {lambda}{sub P} while limiting cases, some ofmore » them already known, are recovered when these values obey some specific orderings. The consequence of these results for comparison with existing experiments is discussed at the end of the paper.« less
  • We discuss the role of the proximity force approximation in deriving limits to the existence of Yukawian forces--predicted in the submillimeter range by many unification models--from Casimir force experiments using the sphere-plane geometry. Two forms of this approximation are discussed, the first used in most analyses of the residuals from the Casimir force experiments performed so far, and the second recently discussed in this context in R. Decca et al.[Phys. Rev. D 79, 124021 (2009)]. We show that the former form of the proximity force approximation overestimates the expected Yukawa force and that the relative deviation from the exact Yukawamore » force is of the same order of magnitude, in the realistic experimental settings, as the relative deviation expected between the exact Casimir force and the Casimir force evaluated in the proximity force approximation. This implies both a systematic shift making the actual limits to the Yukawa force weaker than claimed so far, and a degree of uncertainty in the {alpha}-{lambda} plane related to the handling of the various approximations used in the theory for both the Casimir and the Yukawa forces. We further argue that the recently discussed form for the proximity force approximation is equivalent, for a geometry made of a generic object interacting with an infinite planar slab, to the usual exact integration of any additive two-body interaction, without any need to invoke approximation schemes. If the planar slab is of finite size, an additional source of systematic error arises due to the breaking of the planar translational invariance of the system, and we finally discuss to what extent this may affect limits obtained on power-law and Yukawa forces.« less