相关论文: Functional determinants and Casimir energy in high…

The vacuum expectation value of the surface energy-momentum tensor is evaluated for a scalar field obeying Robin boundary condition on a spherical brane in (D+1)-dimensional spacetime $Ri\times S^{D-1}$, where $Ri$ is a two-dimensional…

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy…

In dimensions d= 1, 2, 3 the Laplacian can be perturbed by a point potential. In higher dimensions the Laplacian with a point potential cannot be defined as a self-adjoint operator. However, for any dimension there exists a natural family…

Let X be a compact Riemannian manifold of dimension two or three and let P be a point of X. We derive comparison formulas relating the zeta-regularized determinant of an arbitrary self-adjoint extension of (symmetric) Laplace operator with…

A general calculation of Casimir energies --in an arbitrary number of dimensions-- for massless quantized fields in spherically symmetric cavities is carried out. All the most common situations, including scalar and spinor fields, the…

We explore the properties of an analog to the Casimir effect on Laakso spaces such as the dependence on the separation of the plates and boundary effects. We also mention some results on the influence of complex poles in the spectral zeta…

We evaluate zeta-functions $\zeta(s)$ at $s=0$ for invariant non-minimal 2nd-order vector and tensor operators defined on maximally symmetric even dimensional spaces. We decompose the operators into their irreducible parts and obtain their…

It is the aim of these lectures to introduce some basic zeta functions and their uses in the areas of the Casimir effect and Bose-Einstein condensation. A brief introduction into these areas is given in the respective sections. We will…

We present a simple formalism for the evaluation of the Casimir energy for two spheres and a sphere and a plane, in case of a scalar fluctuating field, valid at any separations. We compare the exact results with various approximation…

In this paper we propose an approach of obtaining of N-dimensional spherical harmonics based exclusively on the methods of solutions of differential equations and the use of the special functions properties. We deduce the Laplace-Beltrami…

We compute the Casimir energy of a real scalar field in the presence of a pair of partially transparent plane mirrors, modeled by Dirac delta potentials.

Let $M$ denote a finite volume, non-compact Riemann surface without elliptic points, and let $B$ denote the Lax-Phillips scattering operator. Using the superzeta function approach due to Voros, we define a Hurwitz-type zeta function…

In this work we analyze the Casimir energy and force for a scalar field endowed with general self-adjoint boundary conditions propagating in a higher dimensional piston configuration. The piston is constructed as a direct product $I\times…

Further thermodynamic investigations into the behaviour of a polar dielectric working fluid under non-equilibrium and negative pressure conditions are reported. The establishment of a long-range van der Waals interaction between clathrate…

The finite-temperature one-loop effective potential for a scalar field in the static de Sitter space-time is obtained. Within this framework, by using zeta-function regularization, one can get, in the conformally invariant case, the…

The Casimir force on two-dimensional pistons for massive scalar fields with both Dirichlet and hybrid boundary conditions is computed. The physical result is obtained by making use of generalized $\zeta$-function regularization technique.…

Spectral boundary conditions for Laplace-type operators, of interest in string and brane theory, are partly Dirichlet, partly Neumann-type conditions, partitioned by a pseudodifferential projection. We give sufficient conditions for…

We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of…

This paper is devoted to optimal functional inequalities for fractional Laplace operators on the sphere. Based on spectral properties, subcritical inequalities are established. Their consequences for fractional heat flows are considered.…

The effective one-loop potential on $R^{m+1}\times S^N$ spaces for massless tensor fields is evaluated. The Casimir energy is given as a value of $\zeta-$ function by means of which regularization is made. In even- dimensional spaces the…