267 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
SCOZA for Monolayer Films
We show the way in which the self-consistent Ornstein-Zernike approach
(SCOZA) to obtaining structure factors and thermodynamics for Hamiltonian
models can best be applied to two-dimensional systems such as thin films. We
use the nearest-neighbor lattice gas on a square lattice as an illustrative
example.Comment: 10 pages, 5 figure
Self-consistent Ornstein-Zernike approximation for molecules with soft cores
The Self-Consistent Ornstein-Zernike Approximation (SCOZA) is an accurate
liquid state theory. So far it has been tied to interactions composed of hard
core repulsion and long-range attraction, whereas real molecules have soft core
repulsion at short distances. In the present work, this is taken into account
through the introduction of an effective hard core with a diameter that depends
upon temperature only. It is found that the contribution to the configurational
internal energy due to the repulsive reference fluid is of prime importance and
must be included in the thermodynamic self-consistency requirement on which
SCOZA is based. An approximate but accurate evaluation of this contribution
relies on the virial theorem to gauge the amplitude of the pair distribution
function close to the molecular surface. Finally, the SCOZA equation is
transformed by which the problem is reformulated in terms of the usual SCOZA
with fixed hard core reference system and temperature-dependent interaction
The Reality of Casimir Friction
For more than 35 years theorists have studied quantum or Casimir friction,
which occurs when two smooth bodies move transversely to each other,
experiencing a frictional dissipative force due to quantum electromagnetic
fluctuations, which break time-reversal symmetry. These forces are typically
very small, unless the bodies are nearly touching, and consequently such
effects have never been observed, although lateral Casimir forces have been
seen for corrugated surfaces. Partly because of the lack of contact with
phenomena, theoretical predictions for the frictional force between parallel
plates, or between a polarizable atom and a metallic plate, have varied widely.
Here we review the history of these calculations, show that theoretical
consensus is emerging, and offer some hope that it might be possible to
experimentally confirm this phenomenon of dissipative quantum electrodynamics.Comment: 12 pages, 2 figure
The Casimir Problem of Spherical Dielectrics: Quantum Statistical and Field Theoretical Approaches
The Casimir free energy for a system of two dielectric concentric nonmagnetic
spherical bodies is calculated with use of a quantum statistical mechanical
method, at arbitrary temperature. By means of this rather novel method, which
turns out to be quite powerful (we have shown this to be true in other
situations also), we consider first an explicit evaluation of the free energy
for the static case, corresponding to zero Matsubara frequency ().
Thereafter, the time-dependent case is examined. For comparison we consider the
calculation of the free energy with use of the more commonly known field
theoretical method, assuming for simplicity metallic boundary surfaces.Comment: 31 pages, LaTeX, one new reference; version to appear in Phys. Rev.
Casimir Friction Force and Energy Dissipation for Moving Harmonic Oscillators
The Casimir friction problem for a pair of dielectric particles in relative
motion is analyzed, utilizing a microscopic model in which we start from
statistical mechanics for harmonically oscillating particles at finite
temperature moving nonrelativistically with constant velocity. The use of
statistical mechanics in this context has in our opinion some definite
advantages, in comparison with the more conventional quantum electrodynamic
description of media that involves the use of a refractive index. The
statistical-mechanical description is physical and direct, and the oscillator
model, in spite of its simplicity, is nevertheless able to elucidate the
essentials of the Casimir friction. As is known, there are diverging opinions
about this kind of friction in the literature. Our treatment elaborates upon,
and extends, an earlier theory presented by us back in 1992. There we found a
finite friction force at any finite temperature, whereas at zero temperature
the model led to a zero force. As an additional development in the present
paper we evaluate the energy dissipation making use of an exponential cutoff
truncating the relative motion of the oscillators. For the dissipation we also
establish a general expression that is not limited to the simple oscillator
model.Comment: 12 pages, no figures. Discussion extended, references added. To
appear in Europhysics Letter
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