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-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

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

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 energy of a dilute dielectric ball with uniform velocity of light at finite temperature

The Casimir energy, free energy and Casimir force are evaluated, at arbitrary finite temperature, for a dilute dielectric ball with uniform velocity of light inside the ball and in the surrounding medium. In particular, we investigate the classical limit at high temperature. The Casimir force found is repulsive, as in previous calculations.Comment: 15 pages, 1 figur

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

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 ($n=0$). 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.