Leading- and next-to-leading-order lateral Casimir force on corrugated surfaces

TL;DR

This paper derives explicit formulas for the lateral Casimir force between corrugated surfaces, including leading and next-to-leading order terms, using multiple scattering formalism and perturbation theory.

Contribution

It provides the first analytic expressions for the lateral Casimir force on corrugated surfaces at different orders, advancing theoretical understanding.

Findings

Explicit formulas for lateral Casimir force on corrugated surfaces.

Leading order for concentric cylinders, next-to-leading for parallel plates.

Use of multiple scattering formalism and perturbative expansion.

Abstract

We derive explicit analytic expressions for the lateral force for two different configurations with corrugations, parallel plates and concentric cylinders. By making use of the multiple scattering formalism, we calculate the force for a scalar field under the influence of a delta-function potential that has sinusoidal dependence in one direction simulating the corrugations. By making a perturbative expansion in the amplitude of the corrugation we find the leading order for the corrugated concentric cylinders and the next-to-leading order for the corrugated parallel plates.