10 research outputs found

### Whightman function and scalar Casimir densities for a wedge with a cylindrical boundary

Whightman function, vacuum expectation values of the field square, and the
energy-momentum tensor are investigated for a scalar field inside a wedge with
and without a coaxial cylindrical boundary. Dirichlet boundary conditions are
assumed on the bounding surfaces. The vacuum energy-momentum tensor is
evaluated in the general case of the curvature coupling parameter. Making use
of a variant of the generalized Abel-Plana formula, expectation values are
presented as the sum of two terms. The first one corresponds to the geometry
without a cylindrical boundary and the second one is induced by the presence of
this boundary. The asymptotic behaviour of the field square, vacuum energy
density and stresses near the boundaries are investigated. The additional
vacuum forces acting on the wedge sides due the presence of the cylindrical
boundary are evaluated and it is shown that these forces are attractive. As a
limiting case, the geometry of two parallel plates perpendicularly intersected
by a third one is analyzed.Comment: 19 pages, 6 figures, new section is added on the VEVs for the region
outside the cylidrical shell, discussion and references added, accepted for
publication in J. Phys.

### Vacuum polarization induced by a cylindrical boundary in the cosmic string spacetime

In this paper we investigate the Wightman function, the renormalized vacuum
expectation values of the field square, and the energy-momentum tensor for a
massive scalar field with general curvature coupling inside and outside of a
cylindrical shell in the generalized spacetime of straight cosmic string. For
the general case of Robin boundary condition, by using the generalized
Abel-Plana formula, the vacuum expectation values are presented in the form of
the sum of boundary-free and boundary-induced parts. The asymptotic behavior of
the vacuum expectation values of the field square, energy density and stresses
are investigated in various limiting cases. The generalization of the results
to the exterior region is given for a general cylindrically symmetric static
model of the string core with finite support.Comment: 21 pages, 5 figure

### Scalar Casimir densities for cylindrically symmetric Robin boundaries

Wightman function, the vacuum expectation values of the field square and the
energy-momentum tensor are investigated for a massive scalar field with general
curvature coupling parameter in the region between two coaxial cylindrical
boundaries. It is assumed that the field obeys general Robin boundary
conditions on bounding surfaces. The application of a variant of the
generalized Abel-Plana formula allows to extract from the expectation values
the contribution from single shells and to present the interference part in
terms of exponentially convergent integrals. The vacuum forces acting on the
boundaries are presented as the sum of self-action and interaction terms. The
first one contains well-known surface divergences and needs a further
renormalization. The interaction forces between the cylindrical boundaries are
finite and are attractive for special cases of Dirichlet and Neumann scalars.
For the general Robin case the interaction forces can be both attractive or
repulsive depending on the coefficients in the boundary conditions. The total
Casimir energy is evaluated by using the zeta function regularization
technique. It is shown that it contains a part which is located on bounding
surfaces. The formula for the interference part of the surface energy is
derived and the energy balance is discussed.Comment: 22 pages, 5 figure

### Exact zero-point interaction energy between cylinders

We calculate the exact Casimir interaction energy between two perfectly
conducting, very long, eccentric cylindrical shells using a mode summation
technique. Several limiting cases of the exact formula for the Casimir energy
corresponding to this configuration are studied both analytically and
numerically. These include concentric cylinders, cylinder-plane, and eccentric
cylinders, for small and large separations between the surfaces. For small
separations we recover the proximity approximation, while for large separations
we find a weak logarithmic decay of the Casimir interaction energy, typical of
cylindrical geometries.Comment: 20 pages, 7 figure