Spectral Zeta Functions for a Cylinder and a Circle

Spectral zeta functions $\zeta(s)$ for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the complex plane s containing the closed interval of real axis $-1\le$ Re $s \le 0$. Proceeding from this the spectral zeta functions for the boundary conditions given on a circle (boundary value problem on a plane) are obtained without any additional calculations. The Casimir energy for the relevant field configurations is deduced.Comment: REVTeX4, 13 pages, no tables and figures; v2 some misprints are correcte

Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk

We prove an upper bound for the $\varepsilon$-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to $\mathsf{T}_{\mathsf{RW}(G)}\ln(|V|/\varepsilon)$, where |V| is the number of vertices in G, and $\mathsf{T}_{\mathsf{RW}(G)}$ is the 1/4-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clusters, the giant component of the Erdos-Renyi random graph and Poisson point processes in $\mathbb{R}^d$. Our technical tools include a variant of Morris's chameleon process.Comment: Published in at http://dx.doi.org/10.1214/11-AOP714 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The closed piecewise uniform string revisited

We reconsider the composite string model introduced {30 years ago} to study the vacuum energy. The model consists of a scalar field, describing the transversal vibrations of a string consisting of piecewise constant sections with different tensions and mass densities, keeping the speed of light constant across the junctions. We consider the spectrum using transfer matrices and Chebyshev polynomials to get a closed formula for the eigenfrequencies. We calculate vacuum and free energy as well as the entropy of this system in two approaches, one using contour integration and another one using a Hurwitz zeta function. The latter results in a representation in terms of finite sums over polynomials. Several limiting cases are considered as well, for instance, the high-temperature expansion, which is expressed in terms of the heat kernel coefficients. The vacuum energy has no ultraviolet divergences, and the corresponding heat kernel coefficient $a_1$ is zero due to the constancy of the speed of light. This is in parallel to a similar situation in macroscopic electrodynamics with isorefractive boundary conditions.Comment: 12 page

Dispersion Forces Between Fields Confined to Half Spaces

We consider the Casimir effect for a scalar field interacting with another scalar field that is confined to two half spaces. This model is aimed to mimic the interaction of the photon field with matter in two slabs. We use Dirichlet boundary conditions on the interfaces for the fields in the half spaces and calculate their one-loop contribution to the wave equation for the other field. We perform the ultraviolet renormalization and develop a convenient formalism for the calculation of the vacuum energy in this configuration

Electromagnetic Waves from Pulsars Generated by Null Cosmic Strings

Null cosmic strings disturb electromagnetic (EM) fields of charged sources and sources with magnetic moments. As has been recently shown, these perturbations result in a self-force acting on the sources and create EM waves outgoing from the sources. We develop an analytic approximation for asymptotic of the EM waves at the future null infinity and calculate radiation fluxes for sources of the both types. For magnetic-dipole-like sources the radiation flux depends on orientation of the magnetic moment with respect to the string. Estimates show that the peak power of the radiation can be quite large for null strings moving near pulsars and considerably large in case of magnetars. The string generated variations of the luminosities of the stars can be used as a potential experimental signature of null cosmic strings.Comment: 25 pages, 5 figure