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Title: Thermal quantum field theory and the Casimir interaction between dielectrics

Abstract

The Casimir and van der Waals interaction between two dissimilar thick dielectric plates is reconsidered on the basis of thermal quantum field theory in Matsubara formulation. We briefly review two main derivations of the Lifshitz formula in the framework of thermal quantum field theory without use of the fluctuation-dissipation theorem. A set of special conditions is formulated under which these derivations remain valid in the presence of dissipation. The low-temperature behavior of the Casimir and van der Waals interactions between dissimilar dielectrics is found analytically from the Lifshitz theory for both an idealized model of dilute dielectrics and for real dielectrics with finite static dielectric permittivities. The free energy, pressure, and entropy of the Casimir and van der Waals interactions at low temperatures demonstrate the same universal dependence on the temperature as was previously discovered for ideal metals. The entropy vanishes when temperature goes to zero proving the validity of the Nernst heat theorem. This solves the long-standing problem on the consistency of the Lifshitz theory with thermodynamics in the case of dielectric plates. The obtained asymptotic expressions are compared with numerical computations for both dissimilar and similar real dielectrics and found to be in excellent agreement. The role ofmore » the zero-frequency term in Matsubara sum is investigated in the case of dielectric plates. It is shown that the inclusion of conductivity in the model of dielectric response leads to the violation of the Nernst heat theorem. The applications of this result to the topical problems of noncontact atomic friction and the Casimir interaction between real metals are discussed.« less

Authors:
; ;  [1]
  1. Center of Theoretical Studies and Institute for Theoretical Physics, Leipzig University, Augustusplatz 10/11, D-04109 Leipzig (Germany)
Publication Date:
OSTI Identifier:
20713763
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 72; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.72.085009; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BASIC INTERACTIONS; CASIMIR EFFECT; DIELECTRIC MATERIALS; ENTROPY; FLUCTUATIONS; FREE ENERGY; NERNST HEAT THEOREM; PERMITTIVITY; PLATES; QUANTUM ELECTRODYNAMICS; THERMAL CONDUCTIVITY; THERMODYNAMICS; VAN DER WAALS FORCES

Citation Formats

Geyer, B, Klimchitskaya, G L, and Mostepanenko, V M. Thermal quantum field theory and the Casimir interaction between dielectrics. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.085009.
Geyer, B, Klimchitskaya, G L, & Mostepanenko, V M. Thermal quantum field theory and the Casimir interaction between dielectrics. United States. https://doi.org/10.1103/PhysRevD.72.085009
Geyer, B, Klimchitskaya, G L, and Mostepanenko, V M. 2005. "Thermal quantum field theory and the Casimir interaction between dielectrics". United States. https://doi.org/10.1103/PhysRevD.72.085009.
@article{osti_20713763,
title = {Thermal quantum field theory and the Casimir interaction between dielectrics},
author = {Geyer, B and Klimchitskaya, G L and Mostepanenko, V M},
abstractNote = {The Casimir and van der Waals interaction between two dissimilar thick dielectric plates is reconsidered on the basis of thermal quantum field theory in Matsubara formulation. We briefly review two main derivations of the Lifshitz formula in the framework of thermal quantum field theory without use of the fluctuation-dissipation theorem. A set of special conditions is formulated under which these derivations remain valid in the presence of dissipation. The low-temperature behavior of the Casimir and van der Waals interactions between dissimilar dielectrics is found analytically from the Lifshitz theory for both an idealized model of dilute dielectrics and for real dielectrics with finite static dielectric permittivities. The free energy, pressure, and entropy of the Casimir and van der Waals interactions at low temperatures demonstrate the same universal dependence on the temperature as was previously discovered for ideal metals. The entropy vanishes when temperature goes to zero proving the validity of the Nernst heat theorem. This solves the long-standing problem on the consistency of the Lifshitz theory with thermodynamics in the case of dielectric plates. The obtained asymptotic expressions are compared with numerical computations for both dissimilar and similar real dielectrics and found to be in excellent agreement. The role of the zero-frequency term in Matsubara sum is investigated in the case of dielectric plates. It is shown that the inclusion of conductivity in the model of dielectric response leads to the violation of the Nernst heat theorem. The applications of this result to the topical problems of noncontact atomic friction and the Casimir interaction between real metals are discussed.},
doi = {10.1103/PhysRevD.72.085009},
url = {https://www.osti.gov/biblio/20713763}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 72,
place = {United States},
year = {2005},
month = {10}
}