743 research outputs found
Casimir Effect for the Piecewise Uniform String
The Casimir energy for the transverse oscillations of a piecewise uniform
closed string is calculated. In its simplest version the string consists of two
parts I and II having in general different tension and mass density, but is
always obeying the condition that the velocity of sound is equal to the
velocity of light. The model, first introduced by Brevik and Nielsen in 1990,
possesses attractive formal properties implying that it becomes easily
regularizable by several methods, the most powerful one being the contour
integration method. We also consider the case where the string is divided into
2N pieces, of alternating type-I and type-II material. The free energy at
finite temperature, as well as the Hagedorn temperature, are found. Finally, we
make some remarks on the relationship between this kind of theory and the
theory of quantum star graphs, recently considered by Fulling et al.Comment: 10 pages, 1 figure, Submitted to the volume "Cosmology, Quantum
Vacuum, and Zeta Functions", in honour of Professor Emilio Elizalde on the
occasion of his 60th birthda
Two-Brane Randall-Sundrum Model in AdS_5 and dS_5
Two flat Randall - Sundrum three-branes are analyzed, at fixed mutual
distance, in the case where each brane contains an ideal isotropic fluid. Both
fluids are to begin with assumed to obey the equation of state p=(\gamma
-1)\rho, where \gamma is a constant. Thereafter, we impose the condition that
there is zero energy flux from the branes into the bulk, and assume that the
tension on either brane is zero. It then follows that constant values of the
fluid energies at the branes are obtained only if the value of \gamma is equal
to zero (i.e., a `vacuum' fluid). The fluids on the branes are related: if one
brane is a dS_4 brane (the effective four-dimensional constant being positive),
then the other brane is dS_4 also, and if the fluid energy density on one brane
is positive, the energy density on the other brane is larger in magnitude but
negative. This is a non-acceptable result, which sheds some light on how far it
is possible to give a physical interpretation of the two-brane scenario. Also,
we discuss the graviton localization problem in the two-brane setting,
generalizing prior works.Comment: 12 pages, no figures; revised discussion in section III on negative
energy densitie
Casimir Surface Force on a Dilute Dielectric Ball
The Casimir surface force density F on a dielectric dilute spherical ball of
radius a, surrounded by a vacuum, is calculated at zero temperature. We treat
(n-1) (n being the refractive index) as a small parameter. The dispersive
properties of the material are taken into account by adopting a simple
dispersion relation, involving a sharp high frequency cutoff at omega =
omega_0. For a nondispersive medium there appears (after regularization) a
finite, physical, force F^{nondisp} which is repulsive. By means of a uniform
asymptotic expansion of the Riccati-Bessel functions we calculate F^{nondisp}
up to the fourth order in 1/nu. For a dispersive medium the main part of the
force F^{disp} is also repulsive. The dominant term in F^{disp} is proportional
to (n-1)^2{omega_0}^3/a, and will under usual physical conditions outweigh
F^{nondisp} by several orders of magnitude.Comment: 24 pages, latex, no figures, some additions to the Acknowledments
sectio
Casimir Energy for a Spherical Cavity in a Dielectric: Applications to Sonoluminescence
In the final few years of his life, Julian Schwinger proposed that the
``dynamical Casimir effect'' might provide the driving force behind the
puzzling phenomenon of sonoluminescence. Motivated by that exciting suggestion,
we have computed the static Casimir energy of a spherical cavity in an
otherwise uniform material. As expected the result is divergent; yet a
plausible finite answer is extracted, in the leading uniform asymptotic
approximation. This result agrees with that found using zeta-function
regularization. Numerically, we find far too small an energy to account for the
large burst of photons seen in sonoluminescence. If the divergent result is
retained, it is of the wrong sign to drive the effect. Dispersion does not
resolve this contradiction. In the static approximation, the Fresnel drag term
is zero; on the mother hand, electrostriction could be comparable to the
Casimir term. It is argued that this adiabatic approximation to the dynamical
Casimir effect should be quite accurate.Comment: 23 pages, no figures, REVTe
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
Two-Fluid Viscous Modified Gravity on a RS Brane
Singularities in the dark energy late universe are discussed, under the
assumption that the Lagrangian contains the Einstein term R plus a modified
gravity term R^\alpha, where \alpha is a constant. The 4D fluid is taken to be
viscous and composed of two components, one Einstein component where the bulk
viscosity is proportional to the scalar expansion \theta, and another modified
component where the bulk viscosity is proportional to the power
\theta^{2\alpha-1}. Under these conditions it is known from earlier that the
bulk viscosity can drive the fluid from the quintessence region (w > -1) into
the phantom region (w<-1), where w is the thermodynamical parameter [I. Brevik,
Gen. Rel. Grav. 38, 1317 (2006)]. We combine this 4D theory with the 5D
Randall-Sundrum II theory in which there is a single spatially flat brane
situated at y=0. We find that the Big Rip singularity, which occurs in 4D
theory if \alpha >1/2, carries over to the 5D metric in the bulk, |y|>0. The
present investigation generalizes that of an earlier paper [I. Brevik,
arXiv:0807.1797; to appear in Eur. Phys. J. C] in which only a one-component
modified fluid was present.Comment: 8 pages, no figures; to appear in Gravitation & Cosmolog
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.
Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder
Using the mode-by-mode summation technique the zero point energy of the
electromagnetic field is calculated for the boundary conditions given on the
surface of an infinite solid cylinder. It is assumed that the dielectric and
magnetic characteristics of the material which makes up the cylinder
and of that which makes up the surroundings obey the relation . With this
assumption all the divergences cancel. The divergences are regulated by making
use of zeta function techniques. Numerical calculations are carried out for a
dilute dielectric cylinder and for a perfectly conducting cylindrical shell.
The Casimir energy in the first case vanishes, and in the second is in complete
agreement with that obtained by DeRaad and Milton who employed a Green's
function technique with an ultraviolet regulator.Comment: REVTeX, 16 pages, no figures and tables; transcription error in
previous version corrected, giving a zero Casimir energy for a tenuous
cylinde
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