Abstract
The microscopic mechanisms for universality of Casimir forces between macroscopic conductors are displayed in a model of classical charged fluids. The model consists of two slabs in empty space at distance d containing classical charged particles in thermal equilibrium (plasma, electrolyte). A direct computation of the average force per unit surface yields, at large distance, the usual form of the Casimir force in the classical limit (up to a factor 2 due to the fact that the model does not incorporate the magnetic part of the force). Universality originates from perfect screening sum rules obeyed by the microscopic charge correlations in conductors. If one of the slabs is replaced by a macroscopic dielectric medium, the result of Lifshitz theory for the force is retrieved. The techniques used are Mayer expansions and integral equations for charged fluids.
Similar content being viewed by others
References
P. Milonni (1994) The Quantum Vacuum: An Introduction to Quantum Electrodynamics Academic Press San Diego
V.M. Mostepanenko N.N. Trunov (1997) The Casimir Effect and its Applications Clarendon Press Oxford
G. Plunien B. Müller W. Greiner (1986) ArticleTitleThe Casimir effect Phys. Reports. 134 87–193 Occurrence Handle10.1016/0370-1573(86)90020-7 Occurrence Handle1:CAS:528:DyaL28XhsFKqs78%3D
Duplantier B., Rivasseau V., Poincaré Seminar 2002: Vacuum Energy-Renormalization (Progress in Math. Phys., V30.) (Birkhäuser, Basel, 2003)
Balian R., Duplantier B. Electromagnetic Waves Near Perfect Conductors, I. Multiple Scattering Expansions and Distribution of Modes, Ann. Phys. 104:300–335 (1977); II. Casimir Effect, Ann. Phys. 112:165–208 (1978)
EM. Lifshitz (1955) ArticleTitleThe theory of molecular attractive forces between solids J. Exp. Th. Phys. USSR. 29 94–110
Lifshitz EM., Landau L.D., and Pitaevskii LP., Electrodynamics of Continuous Media (Landau course, vol. 8, Pergamon Press, Oxford, 1984), S 90; I. Dzyaloshinskii E., E. Lifshitz M., L. P. Pitaevskii, The General Theory of Van der Waals Forces, Adv. Phys. 10:165–209 (1961)
J. Schwinger (1975) ArticleTitleCasimir effect in source theory Lett. Math. Phys. 1 43–47 Occurrence Handle10.1007/BF00405585
J. Schwinger L.L. DeRaad SuffixJr. KA. Milton (1978) ArticleTitleCasimir effect in dielectrics Ann. Phys. 115 1–23 Occurrence Handle10.1016/0003-4916(78)90172-0 Occurrence Handle1:CAS:528:DyaE1MXkslWhsg%3D%3D
Ph.A. Martin (1988) ArticleTitleSum rules in charged fluids Rev. Mod. Phys. 60 1075–1127 Occurrence Handle10.1103/RevModPhys.60.1075 Occurrence Handle1:CAS:528:DyaL1MXhsVWksrw%3D
PJ. Forrester B. Jancovici G. Téllez (1996) ArticleTitleUniversality in some classical Coulomb systems of restricted dimension J. Stat. Phys. 84 359–378
B. Jancovici G. Téllez (1996) ArticleTitleThe ideal conductor limit J. Phys. A. Math. Gen. 29 1155–1166 Occurrence Handle10.1088/0305-4470/29/6/004
Jancovici B., and Šamaj L., Screening of Casimir forces by electrolytes in semi-infinite geometries, University of Paris-Sud preprint, submitted to JSTAT
Meeron E., Theory of potentials of average force and radial distribution function in ionic solutions, J. Chem. Phys. 28:630–643 (1958); Meeron E., Plasma Physics (McGraw-Hill, New York, 1961)
J.N. Aqua F. Cornu (2003) ArticleTitleDipolar effective interaction in a fluid of charged spheres near a dielectric plate Phys. Rev. E. 68 IssueID026133 1–17 Occurrence Handle10.1103/PhysRevE.68.026133
J.N. Aqua F. Cornu (2001) ArticleTitleDensity profiles in a classical Coulomb fluid near a dielectric wall, I Mean-field scheme. J. Stat. Phys. 105 211–244
J.N. Aqua F. Cornu (2001) ArticleTitleDensity profiles in a classical Coulomb fluid near a dielectric wall, II Weak-coupling systematic expansion J. Stat. Phys. 105 245–283 Occurrence Handle10.1023/A:1012290228733
J.P. Hansen IR. McDonald (1986) Theory of simple liquids Academic Press Second edition
RL. Guernsey (1970) ArticleTitleCorrelation effects in semi-infinite plasmas Phys. Fluids. 13 2089–2102 Occurrence Handle10.1063/1.1693206
B. Jancovici (1982) ArticleTitleClassical coulomb systems near a plane wall. I. J Stat. Phys. 28 43–65 Occurrence Handle10.1007/BF01011622
Cornu F., Correlations in Quantum Plasmas. II. Algebraic Tails, Phys. Rev. E 53:4595–4631 (1996). See also D. Brydges C., Ph. Martin A., Coulomb systems at low density: a review, J. Stat. Phys 96:1163–1330 (1999), sect. VI.A.3
Jackson JD., Classical Electrodynamics (Wiley Text Books, New York, 1998); Schwinger J., L. L. DeRaad Jr., K. A. Milton and W.-Y. Tsai, Classical Electrodynamics (Westview Press, Boulder, 1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Buenzli, P.R., Martin, P.A. Microscopic Origin of Universality in Casimir Forces. J Stat Phys 119, 273–307 (2005). https://doi.org/10.1007/s10955-004-1990-4
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10955-004-1990-4