Nonperturbative approach to Casimir interactions in periodic geometries

Nonperturbative approach to Casimir interactions in periodic geometries

Due to their collective nature Casimir forces can strongly depend on the geometrical shape of the interacting objects. We study the effect of strong periodic shape deformations of two ideal metal plates on their quantum interaction. A nonperturbative approach which is based on a path-integral quantization of the electromagnetic field is presented in detail. Using this approach, we compute the f...

Pseudo-Casimir effect in nematic liquid crystals in frustrating geometries

We study theoretically the fluctuation-induced structural force in nematic systems frustrated by external fields. We focus on the uniform director structure in the hybrid-aligned film characterized by opposing surface fields and in the Freedericksz cell where frustration arises from competing bulk and surface fields. We find that frustration gives rise to several interesting features of the int...

Casimir interactions in graphene systems

The non-retarded Casimir interaction (van der Waals interaction) between two free standing graphene sheets as well as between a graphene sheet and a substrate is determined. We present several different derivations of the interaction. An exact analytical expression is given for the dielectric function of graphene along the imaginary frequency axis within the random phase approximation for arbit...

New geometries in the Casimir effect: Dielectric gratings

An exact solution for the Casimir force between two arbitrary dielectric gratings with the same period d is presented. The Casimir energy for two dielectric gratings or periodic dielectrics is expressed in terms of Rayleigh coefficients. The theory is applied to calculate the Casimir force in several cases of interest.

On nonperturbative localization with quasi - periodic potential