Surface-impedance approach solves problems with the thermal Casimir force between real metals

Journal Article · Sun Jun 01 00:00:00 EDT 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.062102· OSTI ID:20636515

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, 04109 Leipzig (Germany)

The surface-impedance approach to the description of the thermal Casimir effect in the case of real metals is elaborated starting from the free energy of oscillators. The Lifshitz formula expressed in terms of the dielectric permittivity depending only on frequency is shown to be inapplicable in the frequency region where a real current may arise leading to Joule heating of the metal. The standard concept of a fluctuating electromagnetic field on such frequencies meets difficulties when used as a model for the zero-point oscillations or thermal photons in the thermal equilibrium inside metals. Instead, the surface impedance permits not to consider the electromagnetic oscillations inside the metal but taking the realistic material properties into account by means of the effective boundary condition. An independent derivation of the Lifshitz-type formulas for the Casimir free energy and force between two metal plates is presented within the impedance approach. It is shown that they are free of the contradictions with thermodynamics that are specific to the usual Lifshitz formula for dielectrics in combination with the Drude model. We demonstrate that in the impedance approach the zero-frequency contribution is uniquely fixed by the form of impedance function and does not need any of the ad hoc prescriptions intensively discussed in the recent literature. As an example, the computations of the Casimir free energy between two gold plates (or the Casimir force acting between a plate and a sphere) are performed at different separations and temperatures specific for the regions of the anomalous skin effect and infrared optics. The results are in good agreement with those obtained by the use of the tabulated optical data for the complex refraction index and plasma model. It is argued that the surface impedance approach lays a reliable theoretical framework for the future measurements of the thermal Casimir force.

• OSTI ID: 20636515
• Journal Information: Physical Review. A, Vol. 67, Issue 6; Other Information: DOI: 10.1103/PhysRevA.67.062102; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CASIMIR EFFECT
DIELECTRIC MATERIALS
ELECTROMAGNETIC FIELDS
FREE ENERGY
GOLD
IMPEDANCE
JOULE HEATING
OPTICS
OSCILLATIONS
OSCILLATORS
PERMITTIVITY
PHOTONS
PLATES
QUANTUM MECHANICS
SKIN EFFECT
SURFACES
THERMAL EQUILIBRIUM
THERMODYNAMICS