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 of a dilute dielectric ball in the mode summation method

In the $(\epsilon_1-\epsilon_2)^2$--approximation the Casimir energy of a dilute dielectric ball is derived using a simple and clear method of the mode summation. The addition theorem for the Bessel functions enables one to present in a closed form the sum over the angular momentum before the integration over the imaginary frequencies. The linear in $(\epsilon_1-\epsilon_2)$ contribution into the vacuum energy is removed by an appropriate subtraction. The role of the contact terms used in other approaches to this problem is elucidated.Comment: 14 pages, REVTeX, no figures, no tables; presentation is made better, new references are adde

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 $(\epsilon_1, \mu_1)$ and of that which makes up the surroundings $(\epsilon_2, \mu_2)$ obey the relation $\epsilon_1\mu_1= \epsilon_2\mu_2$. 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

Thermodynamic Properties of the 2N-Piece Relativistic String

The thermodynamic free energy F(\beta) is calculated for a gas consisting of the transverse oscillations of a piecewise uniform bosonic string. The string consists of 2N parts of equal length, of alternating type I and type II material, and is relativistic in the sense that the velocity of sound everywhere equals the velocity of light. The present paper is a continuation of two earlier papers, one dealing with the Casimir energy of a 2N--piece string [I. Brevik and R. Sollie (1997)], and another dealing with the thermodynamic properties of a string divided into two (unequal) parts [I. Brevik, A. A. Bytsenko and H. B. Nielsen (1998)]. Making use of the Meinardus theorem we calculate the asymptotics of the level state density, and show that the critical temperatures in the individual parts are equal, for arbitrary spacetime dimension D. If D=26, we find \beta= (2/N)\sqrt{2\pi /T_{II}}, T_{II} being the tension in part II. Thermodynamic interactions of parts related to high genus g is also considered.Comment: 15 pages, LaTeX, 2 figures. Discussion in section 8 expande

Mass and Decay Spectra of the Piecewise Uniform String

Mass and decay spectra are calculated for quantum massive excitations of a piecewise uniform bosonic string. The physical meaning of the critical temperatures characterizing the radiation in the decay of a massive microstate in string theory is discussed.Comment: 7 pages, LaTex, no figure

Randall-Sundrum Model in the Presence of a Brane Bulk Viscosity

The presence of a bulk viscosity for the cosmic fluid on a single Randall-Sundrum brane is considered. The spatial curvature is assumed to be zero. The five-dimensional Friedmann equation is derived, together with the energy conservation equation for the viscous fluid. These governing equations are solved for some special cases: (i) in the low-energy limit when the matter energy density is small compared with brane tension; (ii) for a matter-dominated universe, and (iii) for a radiation-dominated universe. Rough numerical estimates, for the extreme case when the universe is at its Planck time, indicate that the viscous effect can be significant.Comment: 18 pages, RevTeX4, no figures. Discussion in Sec. III expanded; new references. To appear in Phys. Rev.

Thermal Issues in Casimir Forces Between Conductors and Semiconductors

The Casimir effect between metal surfaces has now been well-verified at the few-percent level experimentally. However, the temperature dependence has never been observed in the laboratory, since all experiments are conducted at room temperature. The temperature dependence for the related Casimir-Polder force between an atom and a bulk material has, in contrast, been observed between a BEC and a silica substrate, with the environment and the silica held at different temperatures. There is a controversy about the temperature dependence for the force between metals, having to do with the magnitude of the linear temperature term for both low and high temperature, the latter being most prominent at large distances. There are also related anomalies pertaining to semiconductors. The status of this controversy, and of the relevant experiments, are reviewed in this report.Comment: 8 pages, 4 figures, extended version of presentation at Frontiers of Quantum and Mesoscopic Thermodynamics, Prague, July 2011. Revision corrects some errors in references and minor typographic errors. arXiv admin note: substantial text overlap with arXiv:quant-ph/060500

Viscous Brane Cosmology with a Brane-Bulk Energy Interchange Term

We assume a flat brane located at y=0, surrounded by an AdS space, and consider the 5D Einstein equations when the energy flux component of the energy-momentum tensor is related to the Hubble parameter through a constant Q. We calculate the metric tensor, as well as the Hubble parameter on the brane, when Q is small. As a special case, if the brane is tensionless, the influence from Q on the Hubble parameter is absent. We also consider the emission of gravitons from the brane, by means of the Boltzmann equation. Comparing the energy conservation equation derived herefrom with the energy conservation equation for a viscous fluid on the brane, we find that the entropy change for the fluid in the emission process has to be negative. This peculiar effect is related to the fluid on the brane being a non-closed thermodynamic system. The negative entropy property for non-closed systems is encountered in other areas in physics also, in particular, in connection with the Casimir effect at finite temperature.Comment: 12 pages, latex, no figure