6,572 research outputs found
Pistons modeled by potentials
In this article we consider a piston modelled by a potential in the presence
of extra dimensions. We analyze the functional determinant and the Casimir
effect for this configuration. In order to compute the determinant and Casimir
force we employ the zeta function scheme. Essentially, the computation reduces
to the analysis of the zeta function associated with a scalar field living on
an interval in a background potential. Although, as a model for a
piston, it seems reasonable to assume a potential having compact support within
, we provide a formalism that can be applied to any sufficiently smooth
potential.Comment: 10 pages, LaTeX. A typo in eq. (3.5) has been corrected. In
"Cosmology, Quantum Vacuum and Zeta Functions: In Honour of Emilio Elizalde",
Eds. S.D. Odintsov, D. Saez-Gomez, and S. Xambo-Descamps. (Springer 2011) pp
31
Amplification of the scattering cross section due to non-trivial topology of the spacetime
In previous articles it was demonstrated that the total cross section of the
scattering of two light particles (zero modes of the Kaluza-Klein tower) in the
six-dimensional model differs significantly from the cross
section of the same process in the conventional theory in
four space-time dimensions even for the energies below the threshold of the
first heavy particle. Here the analytical structure of the cross section in the
same model with torus compactification for arbitrary radii of the
two-dimensional torus is studied. Further amplification of the total cross
section due to interaction of the scalar field with constant background Abelian
gauge potential in the space of extra dimensions is shown.Comment: 23 pages, LaTex, 5 figures available on reques
Finite Temperature Casimir Effect in the Presence of Extra Dimensions
We consider the finite temperature Casimir force acting on two parallel
plates in a closed cylinder with the same cross section of arbitrary shape in
the presence of extra dimensions. Dirichlet boundary conditions are imposed on
one plate and fractional Neumann conditions with order between zero (Dirichlet)
and one (Neumann) are imposed on the other plate. Formulas for the Casimir
force show that it is always attractive for Dirichlet boundary conditions, and
is always repulsive when the fractional order is larger than 1/2. For some
fractional orders less than 1/2, the Casimir force can be either attractive or
repulsive depending on the size of the internal manifold and temperature.Comment: To appear in the proceedings of 9th Conference on Quantum Field
Theory under the Influence of External Conditions (QFEXT 09): Devoted to the
Centenary of H. B. G. Casimir, Norman, Oklahoma, 21-25 Sep 200
Scalar Casimir Energies for Separable Coordinate Systems: Application to Semi-transparent Planes in an Annulus
We derive a simplified general expression for the two-body scalar Casimir
energy in generalized separable coordinate systems. We apply this technique to
the case of radial semi-transparent planes in the annular region between two
concentric Dirichlet cylinders. This situation is explored both analytically
and numerically.Comment: 8 pages, 5 figures. Contribution to Proceedings of 9th Conference on
Quantum Field Theory Under the Influence of External Conditions, QFEXT0
Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions
We consider Laplace operators on metric graphs, networks of one-dimensional
line segments (bonds), with matching conditions at the vertices that make the
operator self-adjoint. Such quantum graphs provide a simple model of quantum
mechanics in a classically chaotic system with multiple scales corresponding to
the lengths of the bonds. For graph Laplacians we briefly report results for
the spectral determinant, vacuum energy and heat kernel asymptotics of general
graphs in terms of the vertex matching conditions.Comment: 5 pages, submitted to proceedings of QFEXT09, minor corrections made
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