39 research outputs found
The perfect magnetic conductor (PMC) Casimir piston in d+1 dimensions
Perfect magnetic conductor (PMC) boundary conditions are dual to the more
familiar perfect electric conductor (PEC) conditions and can be viewed as the
electromagnetic analog of the boundary conditions in the bag model for hadrons
in QCD. Recent advances and requirements in communication technologies have
attracted great interest in PMC's and Casimir experiments involving structures
that approximate PMC's may be carried out in the not too distant future. In
this paper, we make a study of the zero-temperature PMC Casimir piston in
dimensions. The PMC Casimir energy is explicitly evaluated by summing over
-dimensional Dirichlet energies where p ranges from 2 to inclusively.
We derive two exact -dimensional expressions for the Casimir force on the
piston and find that the force is negative (attractive) in all dimensions. Both
expressions are applied to the case of 2+1 and 3+1 dimensions. A spin-off from
our work is a contribution to the PEC literature: we obtain a useful
alternative expression for the PEC Casimir piston in 3+1 dimensions and also
evaluate the Casimir force per unit area on an infinite strip, a geometry of
experimental interest.Comment: 18 pages, 1 figure, to appear in Phys. Rev.
Casimir interaction: pistons and cavity
The energy of a perfectly conducting rectangular cavity is studied by making
use of pistons' interactions. The exact solution for a 3D perfectly conducting
piston with an arbitrary cross section is being discussed.Comment: 10 pages, 2 figures, latex2
A thick shell Casimir effect
We consider the Casimir energy of a thick dielectric-diamagnetic shell under
a uniform velocity light condition, as a function of the radii and the
permeabilities. We show that there is a range of parameters in which the stress
on the outer shell is inward, and a range where the stress on the outer shell
is outward. We examine the possibility of obtaining an energetically stable
configuration of a thick shell made of a material with a fixed volume
Demonstration of the asymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime
The measurement of the lateral Casimir force between two aligned sinusoidally
corrugated Au-coated surfaces has been performed in the nonadditive regime. The
use of deeper corrugations also allowed to demonstrate an asymmetry in the
phase dependences of the lateral Casimir force, as predicted earlier. The
measurement data are found to be in excellent agreement with the exact
theoretical results computed at T=300 K including effect of real material
properties. The deviations between the exact theory and the proximity force
approximation are quantified. The obtained results are topical for applications
in nanomachines.Comment: 9 pages, 3 figure
Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit
In this paper, the finite temperature Casimir force acting on a
two-dimensional Casimir piston due to electromagnetic field is computed. It was
found that if mixed boundary conditions are assumed on the piston and its
opposite wall, then the Casimir force always tends to restore the piston
towards the equilibrium position, regardless of the boundary conditions assumed
on the walls transverse to the piston. In contrary, if pure boundary conditions
are assumed on the piston and the opposite wall, then the Casimir force always
tend to pull the piston towards the closer wall and away from the equilibrium
position. The nature of the force is not affected by temperature. However, in
the high temperature regime, the magnitude of the Casimir force grows linearly
with respect to temperature. This shows that the Casimir effect has a classical
limit as has been observed in other literatures.Comment: 14 pages, 3 figures, accepted by Journal of Physics
Pistons modeled by potentials
In this article we consider a piston modelled by a potential in the presence
of extra dimensions. We analyze the functional determinant and the Casimir
effect for this configuration. In order to compute the determinant and Casimir
force we employ the zeta function scheme. Essentially, the computation reduces
to the analysis of the zeta function associated with a scalar field living on
an interval in a background potential. Although, as a model for a
piston, it seems reasonable to assume a potential having compact support within
, we provide a formalism that can be applied to any sufficiently smooth
potential.Comment: 10 pages, LaTeX. A typo in eq. (3.5) has been corrected. In
"Cosmology, Quantum Vacuum and Zeta Functions: In Honour of Emilio Elizalde",
Eds. S.D. Odintsov, D. Saez-Gomez, and S. Xambo-Descamps. (Springer 2011) pp
31
Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region
We suggest a method of construction of general diffeomorphism invariant
boundary conditions for metric fluctuations. The case of dimensional
Euclidean disk is studied in detail. The eigenvalue problem for the Laplace
operator on metric perturbations is reduced to that on -dimensional vector,
tensor and scalar fields. Explicit form of the eigenfunctions of the Laplace
operator is derived. We also study restrictions on boundary conditions which
are imposed by hermiticity of the Laplace operator.Comment: LATeX file, no figures, no special macro
Non-Local Boundary Conditions in Euclidean Quantum Gravity
Non-local boundary conditions for Euclidean quantum gravity are proposed,
consisting of an integro-differential boundary operator acting on metric
perturbations. In this case, the operator P on metric perturbations is of
Laplace type, subject to non-local boundary conditions; by contrast, its
adjoint is the sum of a Laplacian and of a singular Green operator, subject to
local boundary conditions. Self-adjointness of the boundary-value problem is
correctly formulated by looking at Dirichlet-type and Neumann-type realizations
of the operator P, following recent results in the literature. The set of
non-local boundary conditions for perturbative modes of the gravitational field
is written in general form on the Euclidean four-ball. For a particular choice
of the non-local boundary operator, explicit formulae for the boundary-value
problem are obtained in terms of a finite number of unknown functions, but
subject to some consistency conditions. Among the related issues, the problem
arises of whether non-local symmetries exist in Euclidean quantum gravity.Comment: 23 pages, plain Tex. The revised version is much longer, and new
original calculations are presented in section
Lack of strong ellipticity in Euclidean quantum gravity
Recent work in Euclidean quantum gravity has studied boundary conditions
which are completely invariant under infinitesimal diffeomorphisms on metric
perturbations. On using the de Donder gauge-averaging functional, this scheme
leads to both normal and tangential derivatives in the boundary conditions. In
the present paper, it is proved that the corresponding boundary value problem
fails to be strongly elliptic. The result raises deep interpretative issues for
Euclidean quantum gravity on manifolds with boundary.Comment: 14 pages, Plain Tex, 33 KB, no figure
Finite temperature Casimir effect for graphene
We adopt the Dirac model for quasiparticles in graphene and calculate the
finite temperature Casimir interaction between a suspended graphene layer and a
parallel conducting surface. We find that at high temperature the Casimir
interaction in such system is just one half of that for two ideal conductors
separated by the same distance. In this limit single graphene layer behaves
exactly as a Drude metal. In particular, the contribution of the TE mode is
suppressed, while one of the TM mode saturates the ideal metal value. Behaviour
of the Casimir interaction for intermediate temperatures and separations
accessible for an experiment is studied in some detail. We also find an
interesting interplay between two fundamental constants of graphene physics:
the fine structure constant and the Fermi velocity.Comment: 13 pages, 2 figures, to appear in Physical Review