881 research outputs found
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
Casimir energy of a dilute dielectric ball in the mode summation method
In the --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 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
Casimir energy of a non-uniform string
The Casimir energy of a non-uniform string built up from two pieces with
different speed of sound is calculated. A standard procedure of subtracting the
energy of an infinite uniform string is applied, the subtraction being
interpreted as the renormalization of the string tension. It is shown that in
the case of a homogeneous string this method is completely equivalent to the
zeta renormalization.Comment: 11 pages, REVTeX, no figures and table
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
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
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.
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