Casimir Forces: An Exact Approach for Periodically Deformed Objects

TL;DR

This paper introduces an exact, non-perturbative method for calculating Casimir forces between periodically deformed objects, extending beyond traditional two-plate models and accounting for collective fluctuation effects.

Contribution

It presents a novel approach for rigorous Casimir force calculations for disconnected, periodically deformed objects, including non-perturbative effects.

Findings

Force between flat and corrugated plates is always attractive.

Method provides exact results for scalar field Casimir forces.

Extends Casimir force calculations beyond simple geometries.

Abstract

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 pairwise summation of two-body van der Waals forces. 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. In the latter case, the force is found to be always attractive.