Repulsive Casimir forces and the role of surface modes

The Casimir repulsion between a metal and a dielectric suspended in a liquid has been thoroughly studied in recent experiments. In the present paper we consider surface modes in three layered systems modeled by dielectric functions guaranteeing repulsion. It is shown that surface modes play a decisive role in this phenomenon at short separations. For a toy plasma model we find the contribution of the surface modes at all distances.Comment: 13 pages, 3 figures, submitted to PR

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

Sample dependence of the Casimir force

We have analysed available optical data for Au in the mid-infrared range which is important for a precise prediction of the Casimir force. Significant variation of the data demonstrates genuine sample dependence of the dielectric function. We demonstrate that the Casimir force is largely determined by the material properties in the low frequency domain and argue that therefore the precise values of the Drude parameters are crucial for an accurate evaluation of the force. These parameters can be estimated by two different methods, either by fitting real and imaginary parts of the dielectric function at low frequencies, or via a Kramers–Kronig analysis based on the imaginary part of the dielectric function in the extended frequency range. Both methods lead to very similar results. We show that the variation of the Casimir force calculated with the use of different optical data can be as large as 5% and at any rate cannot be ignored. To have a reliable prediction of the force with a precision of 1%, one has to measure the optical properties of metallic films used for the force measurement

On the Casimir entropy for a ball in front of a plane

The violation of the third law of thermodynamics for metals described by the Drude model and for dielectrics with finite \DC conductivity is one of the most interesting problems in the field of the Casimir effect. It manifests itself as a non-vanishing of the entropy for vanishing temperature. We review the relevant calculations for plane surfaces and calculate the corresponding contributions for a ball in front of a plane. In this geometry, these appear in much the same way as for parallel planes. We conclude that the violation of the 3rd law is not related to the infinite size of the planes.Comment: 17 pages, 4 figures, references added, submitted to Phys.Rev.

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

Vacuum energy between a sphere and a plane at finite temperature

We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar and electromagnetic fields and calculate the limiting cases. For small separation we compare the exact results with the corresponding ones obtained in proximity force approximation. For the scalar field with Dirichlet boundary conditions, the low temperature correction is of order $T^2$ like for parallel planes. For the electromagnetic field it is of order $T^4$. For high temperature we observe the usual picture that the leading order is given by the zeroth Matsubara frequency. The non-zero frequencies are exponentially suppressed except for the case of close separation.Comment: 14 pages, 3 figures, revised version with several improvement