2,238 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
Casimir Effects Near the Big Rip Singularity in Viscous Cosmology
Analytical properties of the scalar expansion in the cosmic fluid are
investigated, especially near the future singularity, when the fluid possesses
a constant bulk viscosity \zeta. In addition, we assume that there is a
Casimir-induced term in the fluid's energy-momentum tensor, in such a way that
the Casimir contributions to the energy density and pressure are both
proportional to 1/a^4, 'a' being the scale factor. A series expansion is worked
out for the scalar expansion under the condition that the Casimir influence is
small. Close to the Big Rip singularity the Casimir term has however to fade
away and we obtain the same singular behavior for the scalar expansion, the
scale factor, and the energy density, as in the Casimir-free viscous case.Comment: 7 pages RevTeX, no figures. Minor changes in discussion, some
references added. To appear in Gen. Rel. Gra
Casimir Theory of the Relativistic Composite String Revisited, and a Formally Related Problem in Scalar QFT
The main part of this paper is to present an updated review of the Casimir
energy at zero and finite temperature for the transverse oscillations of a
piecewise uniform closed string. We make use of three different
regularizations: the cutoff method, the complex contour integration method, and
the zeta-function method. The string model is relativistic, in the sense that
the velocity of sound is for each string piece set equal to the velocity of
light. In this sense the theory is analogous to the electromagnetic theory in a
dielectric medium in which the product of permittivity and permeability is
equal to unity (an isorefractive medium). We demonstrate how the formalism
works for a two-piece string, and for a 2N-piece string, and show how in the
latter case a compact recursion relation serves to facilitate the formalism
considerably. The Casimir energy turns out to be negative, and the more so the
larger the number of pieces in the string. The two-piece string is quantized in
D-dimensional spacetime, in the limit when the ratio between the two tensions
is very small. We calculate the free energy and other thermodynamic quantities,
demonstrate scaling properties, and comment on the meaning of the Hagedorn
critical temperature for the two-piece string. Thereafter, as a novel
development we present a scalar field theory for a real field in
three-dimensional space in a potential rising linearly with a longitudinal
coordinate z in the interval 0<z<1, and which is thereafter held constant on a
horizontal plateau. The potential is taken as a rough model of the two-piece
string potential under simplifying conditions, when the length ratio between
the pieces is replaced formally with the mentioned length parameter z.Comment: 24 latex pages, one figure. Contribution to the honorary issue of J.
Phys. A, on the occasion of the 75th anniversary of Professor Stuart Dowker.
The present version, augmented by a section on a related one-dimensional
problem in scalar QFT, matches the forthcoming published versio
Viscosity-Induced Crossing of the Phantom Barrier
We show explicitly, by using astrophysical data plus reasonable assumptions
for the bulk viscosity in the cosmic fluid, how the magnitude of this viscosity
may be high enough to drive the fluid from its position in the quintessence
region at present time across the barrier into the phantom region
in the late universe. The phantom barrier is accordingly not a sharp
mathematical divide, but rather a fuzzy concept. We also calculate the limiting
forms of various thermodynamical quantities, including the rate of entropy
production, for a dark energy fluid near the future Big Rip singularity.Comment: 11 pages, latex, no figures, to appear in Entrop
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
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