Related papers: Using boundary methods to compute the Casimir ener…
The aim of this paper is to show that within the open-system framework the sum-over-modes approach \'a la Casimir leads to the Lifshitz formula for the Casimir free energy. A general result applicable to arbitrary geometries is obtained…
We use the mode summation method together with zeta-function regularization to compute the Casimir energy of a dilute dielectric cylinder. The method is very transparent, and sheds light on the reason the resulting energy vanishes.
We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles non-spheroidal,…
The zero-point energy of a conducting spherical shell is evaluated by imposing boundary conditions on the potential, and on the ghost fields. The scheme requires that temporal and tangential components of perturbations of the potential…
In this paper we describe an approach to Casimir Force problems that is ultimately generalizable to all fields, boundary conditions, and cavity geometries. This approach utilizes locally defined reflection amplitudes to express the energy…
The response of vacuum to the presence of external conditions is the subject of this work. We consider a generalization of the Casimir effect in the presence of curved boundaries on which a sharp potential is concentrated. The profile of…
The energy of a perfectly conducting rectangular cavity is studied by making use of pistons' interactions. The exact solution for a 3D perfectly conducting piston with an arbitrary cross section is being discussed.
We consider the Casimir-Helmholtz free energy at nonzero temperature $T$ for a circular cylinder and perfectly conducting wedge closed by a cylindrical arc, either perfectly conducting or isorefractive. The energy expression at nonzero…
This paper presents comprehensive calculations for thermal and first-order radiative corrections to the Casimir energy in systems involving self-interacting massive and massless scalar fields coupled with {\ae}ther in a fifth compact…
Casimir energy calculations for the conformally coupled massless scalar field for a wedge defined by three intersecting planes and for a pyramid with four triangular surfaces are presented. The group generated by reflections are employed in…
The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches…
The local Casimir energy density and the global Casimir energy for a massless scalar field associated with a $\lambda\delta$-function potential in a 3+1 dimensional circular cylindrical geometry are considered. The global energy is examined…
We present a worldline method for the calculation of Casimir energies for scalar fields coupled to magnetodielectric media. The scalar model we consider may be applied in arbitrary geometries, and it corresponds exactly to one polarization…
In this work, we derive exact self-consistent solutions to the gap equations of the $\mathbb{C}P^{N-1}$ model on a finite interval with Dirichlet boundary conditions in the large-$N$ approximation. The solution reproduce the confining phase…
Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among…
We evaluate the Casimir-Polder potential between two atoms in the presence of an infinite perfectly conducting plate and at nonzero temperature. In order to calculate the potential, we use a method based on equal-time spatial correlations…
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…
Using the formulation of the electromagnetic Green's function of a perfectly conducting cone in terms of analytically continued angular momentum, we compute the Casimir-Polder interaction energy of the cone with a polarizable particle. We…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
We consider a system of three particles, either three identical bosons or two identical fermions plus an impurity, within a three-dimensional isotropic trap interacting via a contact interaction. Using two approaches, one using an infinite…