Thermal quantum field theory and the Casimir interaction between dielectrics

Journal Article · Sat Oct 15 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.085009· OSTI ID:20713763

Geyer, B; Klimchitskaya, G L; Mostepanenko, V M ^[1]

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1. Center of Theoretical Studies and Institute for Theoretical Physics, Leipzig University, Augustusplatz 10/11, D-04109 Leipzig (Germany)

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.

• OSTI ID: 20713763
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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