Casimir forces: An exact approach for periodically deformed objects

A novel approach for calculating Casimir forces between periodically deformed objects is developed. This approach allows, for the first time, a rigorous non-perturbative treatment of the Casimir effect for disconnected objects beyond Casimir's original two-plate configuration. The approach takes into account the collective nature of fluctuation-induced forces, going beyond the commonly used proximity force theorem (PFT) which is a valid approximation for objects with a radius of surface curvature much larger than their distance. As an application of the method, we exactly calculate the Casimir force due to scalar field fluctuations between a flat and a rectangular corrugated plate. Maximal distinction from the PFT towards a much stronger force is found for small corrugation lengths