Casimir forces beyond the proximity approximation

TL;DR

This paper develops a derivative expansion method to improve the accuracy of Casimir force calculations beyond the proximity force approximation, accounting for curvature effects for various boundary conditions and materials.

Contribution

It introduces a systematic approach to include curvature corrections to the PFA for Casimir forces, applicable to different boundary conditions and materials.

Findings

Derived leading curvature corrections to PFA

Provided an accurate force expression valid at all separations

Validated the method for Dirichlet, Neumann, and perfect conductors

Abstract

The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Pad\'e extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere-plate Casimir force at all separations.