Casimir Force between a Half-Space and a Plate of Finite Thickness

Zero-frequency Casimir theory is analyzed from different viewpoints, focusing on the Drude-plasma issue that turns up when one considers thermal corrections to the Casimir force. The problem is that the plasma model, although leaving out dissipation in the material, apparently gives the best agreement with recent experiments. We consider a dielectric plate separated from a dielectric half-space by a vacuum gap, both media being similar. We consider the following categories: (1) Making use of the statistical mechanical method developed by H{\o}ye and Brevik (1998), implying that the quantized electromagnetic field is replaced by interaction between dipole moments oscillating in harmonic potentials, we first verify that the Casimir force is in agreement with the Drude prediction. No use of Fresnel's reflection coefficients is made at this stage. (2) Then turning to the field theoretical description implying use of the reflection coefficients, we derive results in agreement with the forgoing when first setting the frequency equal to zero, before letting the permittivity becoming large. With the plasma relation the reflection coefficient for TE zero frequency modes depend on the component of the wave vector parallel to the surfaces and lies between 0 and 1. This contradicts basic electrostatic theory. (3) Turning to high permeability magnetic materials the TE zero frequency mode describes the static magnetic field in the same way as the TM zero frequency modes describe the static electric fields in electrostatics. With the plasma model magnetic fields, except for a small part, can not pass through metals. i.e.~metals effectively become superconductors. However, recent experimental results clearly favor the plasma model. We shortly discuss a possible explanation for this apparent conflict with electrostatics.Comment: 18 pages latex, no figures, to appear in Phys. Rev.

Self-Consistent Ornstein-Zernike approximation for the Yukawa fluid with improved direct correlation function

Thermodynamic consistency of the Mean Spherical Approximation as well as the Self-Consistent Ornstein-Zernike Approximation (SCOZA) with the virial route to thermodynamics is analyzed in terms of renormalized gamma-ordering. For continuum fluids this suggests the addition of a short-range contribution to the usual SCOZA direct correlation function, and the shift of the adjustable parameter from the potential term to this new term. The range of this contribution is fixed by imposing consistency with the virial route at the critical point. Comparison of the results of our theory for the hard-core Yukawa potential with simulation data show very good agreement for cases where the liquid-vapor transition is stable or not too far into the metastable region with respect to the solid state. In the latter case for extremely short-ranged interactions discrepancies arise.Comment: Minimal changes due to referee's comments. Accepted for publication in J. Chem. Phys