323 research outputs found
On Casimir Pistons
In this paper we study the Casimir force for a piston configuration in
with one dimension being slightly curved and the other two infinite. We work
for two different cases with this setup. In the first, the piston is "free to
move" along a transverse dimension to the curved one and in the other case the
piston "moves" along the curved one. We find that the Casimir force has
opposite signs in the two cases. We also use a semi-analytic method to study
the Casimir energy and force. In addition we discuss some topics for the
aforementioned piston configuration in and for possible modifications
from extra dimensional manifolds.Comment: 20 pages, To be published in MPL
Casimir Energy of a BEC: From Moderate Interactions to the Ideal Gas
Considering the Casimir effect due to phononic excitations of a weakly
interacting dilute {BEC}, we derive a re-normalized expression for the zero
temperature Casimir energy of a {BEC} confined to a parallel
plate geometry with periodic boundary conditions. Our expression is formally
equivalent to the free energy of a bosonic field at finite temperature, with a
nontrivial density of modes that we compute analytically. As a function of the
interaction strength, smoothly describes the transition from
the weakly interacting Bogoliubov regime to the non-interacting ideal {BEC}.
For the weakly interacting case, reduces to leading order to
the Casimir energy due to zero-point fluctuations of massless phonon modes. In
the limit of an ideal Bose gas, our result correctly describes the Casimir
energy going to zero.Comment: 12 pages, 3 figures, accepted for publication in JPA. New version
with corrected typos and an additional appendi
Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions
Finite temperature Casimir theory of the Dirichlet scalar field is developed,
assuming that there is a conventional Casimir setup in physical space with two
infinitely large plates separated by a gap R and in addition an arbitrary
number q of extra compacified dimensions. As a generalization of earlier
theory, we assume in the first part of the paper that there is a scalar
'refractive index' N filling the whole of the physical space region. After
presenting general expressions for free energy and Casimir forces we focus on
the low temperature case, as this is of main physical interest both for force
measurements and also for issues related to entropy and the Nernst theorem.
Thereafter, in the second part we analyze dispersive properties, assuming for
simplicity q=1, by taking into account dispersion associated with the first
Matsubara frequency only. The medium-induced contribution to the free energy,
and pressure, is calculated at low temperatures.Comment: 25 pages, one figure. Minor changes in the discussion. Version to
appear in Physica Script
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
Casimir force on interacting Bose-Einstein condensate
We have presented an analytic theory for the Casimir force on a Bose-Einstein
condensate (BEC) which is confined between two parallel plates. We have
considered Dirichlet boundary conditions for the condensate wave function as
well as for the phonon field. We have shown that, the condensate wave function
(which obeys the Gross-Pitaevskii equation) is responsible for the mean field
part of Casimir force, which usually dominates over the quantum (fluctuations)
part of the Casimir force.Comment: Accepted in Journal of Physics B: Atomic, Molecular and Optical
Physic
Finite Temperature Casimir Effect in Randall-Sundrum Models
The finite temperature Casimir effect for a scalar field in the bulk region
of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the
Casimir energy and the Casimir force for two parallel plates with separation
on the visible brane in the RSI model. High-temperature and low-temperature
cases are covered. Attractiveness versus repulsiveness of the temperature
correction to the force is discussed in the typical special cases of
Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions
at low temperature. The Abel-Plana summation formula is made use of, as this
turns out to be most convenient. Some comments are made on the related
contemporary literature.Comment: 33 pages latex, 2 figures. Some changes in the discussion. To appear
in New J. Phy
Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields
Quantum fluctuations of massless scalar fields represented by quantum
fluctuations of the quasiparticle vacuum in a zero-temperature dilute
Bose-Einstein condensate may well provide the first experimental arena for
measuring the Casimir force of a field other than the electromagnetic field.
This would constitute a real Casimir force measurement - due to quantum
fluctuations - in contrast to thermal fluctuation effects. We develop a
multidimensional cut-off technique for calculating the Casimir energy of
massless scalar fields in -dimensional rectangular spaces with large
dimensions and dimensions of length and generalize the technique to
arbitrary lengths. We explicitly evaluate the multidimensional remainder and
express it in a form that converges exponentially fast. Together with the
compact analytical formulas we derive, the numerical results are exact and easy
to obtain. Most importantly, we show that the division between analytical and
remainder is not arbitrary but has a natural physical interpretation. The
analytical part can be viewed as the sum of individual parallel plate energies
and the remainder as an interaction energy. In a separate procedure, via
results from number theory, we express some odd-dimensional homogeneous Epstein
zeta functions as products of one-dimensional sums plus a tiny remainder and
calculate from them the Casimir energy via zeta function regularization.Comment: 42 pages, 3 figures. v.2: typos corrected to match published versio
Casimir Effect in closed spaces
As it is well known the topology of space is not totally determined by
Einstein's equations. It is considered a massless scalar quantum field in a
static Euclidean space of dimension 3. The expectation value for the energy
density in all compact orientable Euclidean 3-spaces are obtained in this work
as a finite summation of Epstein type zeta functions. The Casimir energy
density for these particular manifolds is independent of the type of coupling
with curvature. A numerical plot of the result inside each Dirichlet region is
obtained.Comment: Version accepted for publication. The most general coupling with
curvature is chose
Boundary Shape and Casimir Energy
Casimir energy changes are investigated for geometries obtained by small but
arbitrary deformations of a given geometry for which the vacuum energy is
already known for the massless scalar field. As a specific case, deformation of
a spherical shell is studied. From the deformation of the sphere we show that
the Casimir energy is a decreasing function of the surface to volume ratio. The
decreasing rate is higher for less smooth deformations.Comment: 12 page
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