193 research outputs found
The few-body problem in terms of correlated gaussians
In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic
Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer,
Berlin, 1998)] present the stochastic variational method in a very exhaustive
way. In this framework, the so-called correlated gaussian bases are often
employed. General formulae for the matrix elements of various operators can be
found in the textbook. However the Fourier transform of correlated gaussians
and their application to the management of a relativistic kinetic energy
operator are missing and cannot be found in the literature. In this paper we
present these interesting formulae. We give also a derivation for new
formulations concerning central potentials; the corresponding formulae are more
efficient numerically than those presented in the textbook.Comment: 10 page
The heat kernel coefficients for the dielectric cylinder
We calculate the \hkks for the \elm field in the background of a dielectric
cylinder with non equal speeds of light inside and outside. The coefficient
whose vanishing makes the vacuum energy of a massless field unique,
turns out to be zero in dilute order, i.e., in order (\ep-1)^{2}, and nonzero
beyond. As a consequence, the vanishing of the vacuum energy in the presence of
a dielectric cylinder found by Casimir-Polder summation must take place
irrespectively of the methods by which it might be calculated.Comment: 14 pages, 1 figur
Electromagnetic wave scattering by a superconductor
The interaction between radiation and superconductors is explored in this
paper. In particular, the calculation of a plane standing wave scattered by an
infinite cylindrical superconductor is performed by solving the Helmholtz
equation in cylindrical coordinates. Numerical results computed up to
of Bessel functions are presented for different wavelengths
showing the appearance of a diffraction pattern.Comment: 3 pages, 3 figure
Wightman function and Casimir densities for Robin plates in the Fulling-Rindler vacuum
Wightman function, the vacuum expectation values of the field square and the
energy-momentum tensor are investigated for a massive scalar field with an
arbitrary curvature coupling parameter in the region between two infinite
parallel plates moving by uniform proper acceleration. We assume that the field
is prepared in the Fulling-Rindler vacuum state and satisfies Robin boundary
conditions on the plates. The mode-summation method is used with a combination
of a variant of the generalized Abel-Plana formula. This allows to extract
manifestly the contributions to the expectation values due to a single boundary
and to present the second plate-induced parts in terms of exponentially
convergent integrals. Various limiting cases are investigated. The vacuum
forces acting on the boundaries are presented as a sum of the self-action and
'interaction' terms. The first one contains well known surface divergences and
needs a further renormalization. The 'interaction' forces between the plates
are investigated as functions of the proper accelerations and coefficients in
the boundary conditions. We show that there is a region in the space of these
parameters in which the 'interaction' forces are repulsive for small distances
and attractive for large distances.Comment: 20 pages, 2 figures, discussion added, accepted for publication in
Int. J. Mod. Phys.
Casimir effect of electromagnetic field in D-dimensional spherically symmetric cavities
Eigenmodes of electromagnetic field with perfectly conducting or infinitely
permeable conditions on the boundary of a D-dimensional spherically symmetric
cavity is derived explicitly. It is shown that there are (D-2) polarizations
for TE modes and one polarization for TM modes, giving rise to a total of (D-1)
polarizations. In case of a D-dimensional ball, the eigenfrequencies of
electromagnetic field with perfectly conducting boundary condition coincides
with the eigenfrequencies of gauge one-forms with relative boundary condition;
whereas the eigenfrequencies of electromagnetic field with infinitely permeable
boundary condition coincides with the eigenfrequencies of gauge one-forms with
absolute boundary condition. Casimir energy for a D-dimensional spherical shell
configuration is computed using both cut-off regularization and zeta
regularization. For a double spherical shell configuration, it is shown that
the Casimir energy can be written as a sum of the single spherical shell
contributions and an interacting term, and the latter is free of divergence.
The interacting term always gives rise to an attractive force between the two
spherical shells. Its leading term is the Casimir force acting between two
parallel plates of the same area, as expected by proximity force approximation.Comment: 28 page
Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime
We examine the time evolution of the five-dimensional Einstein field
equations subjected to a flat, anisotropic Robertson-Walker metric, where the
3D and higher-dimensional scale factors are allowed to dynamically evolve at
different rates. By adopting equations of state relating the 3D and
higher-dimensional pressures to the density, we obtain an exact expression
relating the higher-dimensional scale factor to a function of the 3D scale
factor. This relation allows us to write the Friedmann-Robertson-Walker field
equations exclusively in terms of the 3D scale factor, thus yielding a set of
4D effective Friedmann-Robertson-Walker field equations. We examine the
effective field equations in the general case and obtain an exact expression
relating a function of the 3D scale factor to the time. This expression
involves a hypergeometric function and cannot, in general, be inverted to yield
an analytical expression for the 3D scale factor as a function of time. When
the hypergeometric function is expanded for small and large arguments, we
obtain a generalized treatment of the dynamical compactification scenario of
Mohammedi [Phys.Rev.D 65, 104018 (2002)] and the 5D vacuum solution of Chodos
and Detweiler [Phys.Rev.D 21, 2167 (1980)], respectively. By expanding the
hypergeometric function near a branch point, we obtain the perturbative
solution for the 3D scale factor in the small time regime. This solution
exhibits accelerated expansion, which, remarkably, is independent of the value
of the 4D equation of state parameter w. This early-time epoch of accelerated
expansion arises naturally out of the anisotropic evolution of 5D spacetime
when the pressure in the extra dimension is negative and offers a possible
alternative to scalar field inflationary theory.Comment: 20 pages, 4 figures, paper format streamlined with main results
emphasized and details pushed to appendixes, current version matches that of
published versio
Casimir-Polder force density between an atom and a conducting wall
In this paper we calculate the Casimir-Polder force density (force per unit
area acting on the elements of the surface) on a metallic plate placed in front
of a neutral atom. To obtain the force density we use the quantum operator
associated to the electromagnetic stress tensor. We explicitly show that the
integral of this force density over the plate reproduces the total force acting
on the plate. This result shows that, although the force is obtained as a sum
of surface element-atom contributions, the stress-tensor method includes also
nonadditive components of Casimir-Polder forces in the evaluation of the force
acting on a macroscopic object.Comment: 5 page
Study of multi black hole and ring singularity apparent horizons
We study critical black hole separations for the formation of a common
apparent horizon in systems of - black holes in a time symmetric
configuration. We study in detail the aligned equal mass cases for ,
and relate them to the unequal mass binary black hole case. We then study the
apparent horizon of the time symmetric initial geometry of a ring singularity
of different radii. The apparent horizon is used as indicative of the location
of the event horizon in an effort to predict a critical ring radius that would
generate an event horizon of toroidal topology. We found that a good estimate
for this ring critical radius is . We briefly discuss the
connection of this two cases through a discrete black hole 'necklace'
configuration.Comment: 31 pages, 21 figure
The Casimir effect for the Bose-Gas in Slabs
We study the Casimir effect for the perfect Bose-gase in the slab geometry
for various boundary conditions. We show that the grand canonical potential per
unit area at the bulk critical chemical potential has the standard
asymptotic form with universal Casimir terms.Comment: 6 pages, submitted to Europhysics LettersWe study the Casimir effect
for the perfect Bose-gase in the slab geometry for various boundary
conditions. We show that the grand canonical potential per unit area at the
bulk critical chemical potential has the standard asymptotic form
with universal Casimir term
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