240 research outputs found
Casimir Friction Force Between Polarizable Media
This work is a continuation of our recent series of papers on Casimir
friction, for a pair of particles of low relative particle velocity. Each
particle is modeled as a simple harmonic oscillator. Our basic method, as
before, is the use of quantum mechanical statistical mechanics, involving the
Kubo formula, at finite temperature. In this work we begin by analyzing the
Casimir friction between two particles polarizable in all spatial directions,
this being a generalization of our study in EPL 91, 60003 (2010), which was
restricted to a pair of particles with longitudinal polarization only. For
simplicity the particles are taken to interact via the electrostatic
dipole-dipole interaction. Thereafter, we consider the Casimir friction between
one particle and a dielectric half-space, and also the friction between two
dielectric half-spaces. Finally, we consider general polarizabilities (beyond
the simple one-oscillator form), and show how friction occurs at finite
temperature when finite frequency regions of the imaginary parts of
polarizabilities overlap.Comment: 13 pages latex, no figure
Towards a unification of HRT and SCOZA
The Hierarchical Reference Theory (HRT) and the Self-Consistent
Ornstein-Zernike Approximation (SCOZA) are two liquid state theories that both
furnish a largely satisfactory description of the critical region as well as
phase separation and the equation of state in general. Furthermore, there are a
number of similarities that suggest the possibility of a unification of both
theories. As a first step towards this goal we consider the problem of
combining the lowest order gamma expansion result for the incorporation of a
Fourier component of the interaction with the requirement of consistency
between internal and free energies, leaving aside the compressibility relation.
For simplicity we restrict ourselves to a simplified lattice gas that is
expected to display the same qualitative behavior as more elaborate models. It
turns out that the analytically tractable Mean Spherical Approximation is a
solution to this problem, as are several of its generalizations. Analysis of
the characteristic equations shows the potential for a practical scheme and
yields necessary conditions any closure to the Ornstein Zernike relation must
fulfill for the consistency problem to be well posed and to have a unique
differentiable solution. These criteria are expected to remain valid for more
general discrete and continuous systems, even if consistency with the
compressibility route is also enforced where possible explicit solutions will
require numerical evaluations.Comment: Minor changes in accordance with referee comment
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.
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