4,893 research outputs found
Surface Divergences and Boundary Energies in the Casimir Effect
Although Casimir, or quantum vacuum, forces between distinct bodies, or
self-stresses of individual bodies, have been calculated by a variety of
different methods since 1948, they have always been plagued by divergences.
Some of these divergences are associated with the volume, and so may be more or
less unambiguously removed, while other divergences are associated with the
surface. The interpretation of these has been quite controversial. Particularly
mysterious is the contradiction between finite total self-energies and surface
divergences in the local energy density. In this paper we clarify the role of
surface divergences.Comment: 8 pages, 1 figure, submitted to proceedings of QFEXT0
On the Bergman-Milton bounds for the homogenization of dielectric composite materials
The Bergman-Milton bounds provide limits on the effective permittivity of a
composite material comprising two isotropic dielectric materials. These provide
tight bounds for composites arising from many conventional materials. We
reconsider the Bergman-Milton bounds in light of the recent emergence of
metamaterials, in which unconventional parameter ranges for relative
permittivities are encountered. Specifically, it is demonstrated that: (a) for
nondissipative materials the bounds may be unlimited if the constituent
materials have relative permittivities of opposite signs; (b) for weakly
dissipative materials characterized by relative permittivities with real parts
of opposite signs, the bounds may be exceedingly large
Green's Dyadic Approach of the Self-Stress on a Dielectric-Diamagnetic Cylinder with Non-Uniform Speed of Light
We present a Green's dyadic formulation to calculate the Casimir energy for a
dielectric-diamagnetic cylinder with the speed of light differing on the inside
and outside. Although the result is in general divergent, special cases are
meaningful. It is pointed out how the self-stress on a purely dielectric
cylinder vanishes through second order in the deviation of the permittivity
from its vacuum value, in agreement with the result calculated from the sum of
van der Waals forces.Comment: 8 pages, submitted to proceedings of QFEXT0
Casimir Energies and Pressures for -function Potentials
The Casimir energies and pressures for a massless scalar field associated
with -function potentials in 1+1 and 3+1 dimensions are calculated. For
parallel plane surfaces, the results are finite, coincide with the pressures
associated with Dirichlet planes in the limit of strong coupling, and for weak
coupling do not possess a power-series expansion in 1+1 dimension. The relation
between Casimir energies and Casimir pressures is clarified,and the former are
shown to involve surface terms. The Casimir energy for a -function
spherical shell in 3+1 dimensions has an expression that reduces to the
familiar result for a Dirichlet shell in the strong-coupling limit. However,
the Casimir energy for finite coupling possesses a logarithmic divergence first
appearing in third order in the weak-coupling expansion, which seems
unremovable. The corresponding energies and pressures for a derivative of a
-function potential for the same spherical geometry generalizes the TM
contributions of electrodynamics. Cancellation of divergences can occur between
the TE (-function) and TM (derivative of -function) Casimir
energies. These results clarify recent discussions in the literature.Comment: 16 pages, 1 eps figure, uses REVTeX
Spectral representation of the effective dielectric constant of graded composites
We generalize the Bergman-Milton spectral representation, originally derived
for a two-component composite, to extract the spectral density function for the
effective dielectric constant of a graded composite. This work has been
motivated by a recent study of the optical absorption spectrum of a graded
metallic film [Applied Physics Letters, 85, 94 (2004)] in which a broad
surface-plasmon absorption band has been shown to be responsible for enhanced
nonlinear optical response as well as an attractive figure of merit. It turns
out that, unlike in the case of homogeneous constituent components, the
characteristic function of a graded composite is a continuous function because
of the continuous variation of the dielectric function within the constituent
components. Analytic generalization to three dimensional graded composites is
discussed, and numerical calculations of multilayered composites are given as a
simple application.Comment: Physical Review E, submitted for publication
Statistical-mechanical theory of the overall magnetic properties of mesocrystals
The mesocrystal showing both electrorheological and magnetorheological
effects is called electro-magnetorheological (EMR) solids. Prediction of the
overall magnetic properties of the EMR solids is a challenging task due to the
coexistence of the uniaxially anisotropic behavior and structural transition as
well as long-range interaction between the suspended particles. To consider the
uniaxial anisotropy effect, we present an anisotropic Kirkwood-Fr\"{o}hlich
equation for calculating the effective permeabilities by adopting an explicit
characteristic spheroid rather than a characteristic sphere used in the
derivation of the usual Kirkwood-Fr\"{o}hlich equation. Further, by applying an
Ewald-Kornfeld formulation we are able to investigate the effective
permeability by including the structural transition and long-range interaction
explicitly. Our theory can reduce to the usual Kirkwood-Fr\"{o}hlich equation
and Onsager equation naturally. To this end, the numerical simulation shows the
validity of monitoring the structure of EMR solids by detecting their effective
permeabilities.Comment: 14 pages, 1 figur
Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
We show that any pair of real symmetric tensors \BGve and \BGm can be
realized as the effective electric permittivity and effective magnetic
permeability of a metamaterial at a given fixed frequency. The construction
starts with two extremely low loss metamaterials, with arbitrarily small
microstructure, whose existence is ensured by the work of Bouchitt{\'e} and
Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a
permittivity tensor with exactly one negative eigenvalue, and a positive
permeability tensor, and the other having a positive permittivity tensor, and a
permeability tensor having exactly one negative eigenvalue. To achieve the
desired effective properties these materials are laminated together in a
hierarchical multiple rank laminate structure, with widely separated length
scales, and varying directions of lamination, but with the largest length scale
still much shorter than the wavelengths and attenuation lengths in the
macroscopic effective medium.Comment: 12 pages, no figure
Scalar Casimir Energies of Tetrahedra
New results for scalar Casimir self-energies arising from interior modes are
presented for the three integrable tetrahedral cavities. Since the eigenmodes
are all known, the energies can be directly evaluated by mode summation, with a
point-splitting regulator, which amounts to evaluation of the cylinder kernel.
The correct Weyl divergences, depending on the volume, surface area, and the
corners, are obtained, which is strong evidence that the counting of modes is
correct. Because there is no curvature, the finite part of the quantum energy
may be unambiguously extracted. Dirichlet and Neumann boundary conditions are
considered and systematic behavior of the energy in terms of geometric
invariants is explored.Comment: Talk given at QFEXT 1
Dirac and Klein-Gordon particles in one-dimensional periodic potentials
We evaluate the dispersion relation for massless fermions, described by the
Dirac equation, and for zero-spin bosons, described by the Klein-Gordon
equation, moving in two dimensions and in the presence of a one-dimensional
periodic potential. For massless fermions the dispersion relation shows a zero
gap for carriers with zero momentum in the direction parallel to the barriers
in agreement with the well-known "Klein paradox". Numerical results for the
energy spectrum and the density of states are presented. Those for fermions are
appropriate to graphene in which carriers behave relativistically with the
"light speed" replaced by the Fermi velocity. In addition, we evaluate the
transmission through a finite number of barriers for fermions and zero-spin
bosons and relate it with that through a superlattice.Comment: 9 pages, 12 figure
Direct mode summation for the Casimir energy of a solid ball
The Casimir energy of a solid ball placed in an infinite medium is calculated
by a direct frequency summation using the contour integration. It is assumed
that the permittivity and permeability of the ball and medium satisfy the
condition . Upon deriving the general
expression for the Casimir energy, a dilute compact ball is considered
. In this case the
calculations are carried out which are of the first order in and take
account of the five terms in the Debye expansion of the Bessel functions
involved. The implication of the obtained results to the attempts of explaining
the sonoluminescence via the Casimir effect is shortly discussed.Comment: REVTeX, 7 pages, no figures and tables, treatment of a dilute
dielectric ball is revised, new references are adde
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