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Title: Comment on 'Low-frequency character of the Casimir force between metallic films'

Abstract

In Phys. Rev. E 70, 047102 (2004), Torgerson and Lamoreaux investigated for the first time the real-frequency spectrum of the finite temperature correction to the Casimir force, for metallic plates of finite conductivity. The very interesting result of this study is that the large correction from the TE mode is dominated by low frequencies, for which the dielectric description of the metal is invalid, and the authors correctly point out that a more realistic description is provided by low-frequency metallic boundary conditions. However, their subsequent analysis uses an incorrect form of metallic boundary conditions for TE modes. After correcting this error, we find that their main conclusion was nevertheless qualitatively correct: contrary to the result of the dielectric model, the thermal TE mode correction leads to an increase in the TE mode force of attraction between the plates. The correction found by us, however, has a magnitude about 20 times larger than that quoted by Torgerson and Lamoreaux.

Authors:
 [1]
  1. Dipartimento di Scienze Fisiche, Universita di Napoli Federico II, Complesso Universitario MSA, Via Cintia, I-80126 Naples (Italy) and INFN, Sezione di Napoli, Naples (Italy)
Publication Date:
OSTI Identifier:
20779253
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevE.73.048101; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; CASIMIR EFFECT; CORRECTIONS; DIELECTRIC MATERIALS; ELECTROMAGNETISM; ERRORS; FILMS; PLATES

Citation Formats

Bimonte, Giuseppe. Comment on 'Low-frequency character of the Casimir force between metallic films'. United States: N. p., 2006. Web. doi:10.1103/PHYSREVE.73.0.
Bimonte, Giuseppe. Comment on 'Low-frequency character of the Casimir force between metallic films'. United States. doi:10.1103/PHYSREVE.73.0.
Bimonte, Giuseppe. Sat . "Comment on 'Low-frequency character of the Casimir force between metallic films'". United States. doi:10.1103/PHYSREVE.73.0.
@article{osti_20779253,
title = {Comment on 'Low-frequency character of the Casimir force between metallic films'},
author = {Bimonte, Giuseppe},
abstractNote = {In Phys. Rev. E 70, 047102 (2004), Torgerson and Lamoreaux investigated for the first time the real-frequency spectrum of the finite temperature correction to the Casimir force, for metallic plates of finite conductivity. The very interesting result of this study is that the large correction from the TE mode is dominated by low frequencies, for which the dielectric description of the metal is invalid, and the authors correctly point out that a more realistic description is provided by low-frequency metallic boundary conditions. However, their subsequent analysis uses an incorrect form of metallic boundary conditions for TE modes. After correcting this error, we find that their main conclusion was nevertheless qualitatively correct: contrary to the result of the dielectric model, the thermal TE mode correction leads to an increase in the TE mode force of attraction between the plates. The correction found by us, however, has a magnitude about 20 times larger than that quoted by Torgerson and Lamoreaux.},
doi = {10.1103/PHYSREVE.73.0},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 4,
volume = 73,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}
  • The frequency spectrum of the finite temperature correction to the Casimir force can be determined by use of the Lifshitz formalism for metallic plates of finite conductivity. We show that the correction for the TE electromagnetic modes is dominated by frequencies so low that the plates cannot be modeled as ideal dielectrics. We also address issues relating to the behavior of electromagnetic fields at the surfaces and within metallic conductors, and calculate the surface modes using appropriate low-frequency metallic boundary conditions. Our result brings the thermal correction into agreement with experimental results that were previously obtained. We suggest a seriesmore » of measurements that will test the veracity of our analysis.« less
  • In a recent paper Geyer, Klimchitskaya, and Mostepanenko [Phys. Rev. A 67, 062102 (2003)] proposed the final solution of the problem of temperature correction to the Casimir force between real metals. The basic idea was that one cannot use the dielectric permittivity in the frequency region where a real current may arise leading to Joule heating of the metal. Instead, the surface impedance approach is proposed as a solution of all contradictions. The purpose of this comment is to show that (i) the main idea contradicts to the fluctuation dissipation theorem (ii) the proposed method to calculate the force givesmore » the wrong value of the temperature correction since the contribution of low frequency fluctuations is calculated with the impedance which is not applicable at low frequencies.« less
  • The preceding Comment discusses in detail the main idea of our paper [Phys. Rev. A 67, 062102 (2003)], namely that one cannot substitute the Drude dielectric function into the Lifshitz formula for the thermal Casimir force in the frequency region where a real current of conduction electrons leads to Joule heating in the metal. In that Comment, it is claimed that this idea would be in contradiction to the fluctuation-dissipation theorem. In this Reply we present an explicit explanation why there is no contradiction. In the second part of the Comment an alternative method is suggested, different from the onemore » used in our paper, to calculate the thermal Casimir force in the framework of the impedance approach. This method is in support of a previous prediction by Svetovoy and Lokhanin, criticized by us, that there exists a relatively large thermal correction to the Casimir force between real metals at small separations. Here we present strong quantitative arguments in favor of the statement that the method of the Comment is in violation of the Nernst heat theorem. We also demonstrate that it is in contradiction with experiment. The approach of our paper is shown to be in agreement with both thermodynamics and experimental data.« less
  • The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for submicron separations. For this purpose it is necessary to estimate very accurately the dielectric function of a conductor along the imaginary frequency axis. This task is complicated in the case of ohmic conductors because optical data do not usually extend to sufficiently low frequencies to permit an accurate evaluation of the standard Kramers-Kronig integral used to compute {epsilon}(i{xi}). By making important improvements to the results of a previous paper bymore » the author, it is shown that this difficulty can be resolved by considering suitable weighted dispersion relations, which strongly suppress the contribution of low frequencies. The weighted dispersion formulas presented in this paper permit us to estimate accurately the dielectric function of ohmic conductors for imaginary frequencies, on the basis of optical data extending from the IR to the UV, with no need for uncontrolled data extrapolations toward zero frequency that are necessary with standard Kramers-Kronig relations. Applications to several sets of data for gold films are presented to demonstrate the viability of the dispersion formulas presented in this paper.« less
  • We study the Casimir force between two corrugated plates due to thermal fluctuations of a scalar field. For arbitrary corrugations and temperature T, we provide an analytical expression for the Casimir force, which is exact to second order in the corrugation amplitude. We study the specific case of two sinusoidally corrugated plates with corrugation wavelength {lambda}, lateral displacement b, and mean separation H. We find that the lateral Casimir force is F{sub l}(T,H)sin(2{pi}b/{lambda}). In other words, at all temperatures, the lateral force is a sinusoidal function of the lateral shift. In the limit {lambda}>>H, F{sub l}(T{yields}{infinity},H){proportional_to}k{sub B}TH{sup -4}{lambda}{sup -1}. Inmore » the opposite limit {lambda}<« less