Related papers: Generating function of the arithmetical function r…
The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is…
Techniques are presented for calculating directly the scalar functional determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions. The method involves a large mass asymptotic limit which is…
When the vacuum is partitioned by material boundaries with arbitrary shape, one can define the zero-point energy and the free energy of the electromagnetic waves in it: this can be done, independently of the nature of the boundaries, in the…
The Casimir effect is an interesting phenomenon in the sense that it provides us with one of the primitive means of extracting the energy out of the vacuum. Since the original work of Casimir a number of works have appeared in extending the…
The zero-point energy of a massless fermion field in the interior of two parallel plates in a D-dimensional space-time at zero temperature is calculated. In order to regularize the model, a mix between dimensional and zeta-function…
Since massive scalar field plays an important role in theoretical physics, we consider the interaction between a sphere and a plate due to the vacuum fluctuation of a massive scalar field. We consider combinations of Dirichlet and Neumann…
This paper is a continuation of a previous one [Jancovici and Samaj, 2004 J. Stat. Mech. P08006] dealing with classical Casimir phenomena in semi-infinite wall geometries. In that paper, using microscopic Coulomb systems, the long-ranged…
We calculate the partition function for "composite particles". For any finite number of states d, and in the following two cases: 1)all states have the same energy, 2)the energy is linearly distributed over the states, we transform the…
The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of…
We compute (as functions of the shape and Wilson-line moduli) the one-loop Casimir energy induced by higher-dimensional supergravities compactified from 6D to 4D on 2-tori, and on some of their Z_N orbifolds. Detailed calculations are given…
We consider the Casimir interaction between two spheres at zero and finite temperature, for both scalar fields and electromagnetic fields. Of particular interest is the asymptotic expansions of the Casimir free energy when the distance…
Casimir energy is calculated for 5D scalar theory in the {\it warped} geometry. A new regularization, called {\it sphere lattice regularization}, is taken. The regularized configuration is {\it closed-string like}. We numerically evaluate…
Within the trln-formalism we investigate the vacuum interaction of cosmic strings and the influence of strings width on this effect. For the massless real scalar field we compute the Casimir contribution into the total vacuum energy. The…
We present an entirely microscopic calculation of the Casimir force $f(d)$ between two metallic plates in the limit of large separation $d$. The models of metals consist of mobile quantum charges in thermal equilibrium with the photon field…
The vacuum fluctuations give rise to a number of phenomena; however, the the Casimir Effect is arguably the most salient manifestation of the quantum vacuum. In its most basic form it is realized through the interaction of a pair of neutral…
The three dimensional mean spherical model on a hypercubic lattice with a film geometry $L\times \infty ^2$ under periodic boundary conditions is considered in the presence of an external magnetic field $H$. The universal Casimir amplitude…
We obtain an hybrid expression for the heat-kernel, and from that the density of the free energy, for a minimally coupled scalar field in a Schwarzschild geometry at finite temperature. This gives us the zero-point energy density as a…
Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…
A piston is introduced into a spherical lune Casimir cavity turning it into two adjacent lunes separated by the (hemispherical) piston. On the basis of zeta function regularisation, the vacuum energy of the arrangement is finite for…
One of the most efficient methods for the evaluation of the vacuum expectation values for physical observables in the Casimir effect is based on using the Abel-Plana summation formula. This enables to derive the renormalized quantities in a…