Beyond the simple Proximity Force Approximation: geometrical effects on the non-retarded Casimir interaction

TL;DR

This paper investigates how complex geometries influence the non-retarded Casimir force beyond the simple proximity force approximation, providing analytical corrections and comparisons with numerical calculations for various shapes.

Contribution

It introduces analytical geometrical correction factors to the PFA for non-retarded Casimir interactions across multiple object shapes, enhancing accuracy over the simple approximation.

Findings

Analytical correction factors for various shapes

Comparison with numerical calculations shows improved accuracy

Provides a comprehensive table of geometrical effects

Abstract

We study the geometrical corrections to the simple Proximity Force Approximation for the non-retarded Casimir force. We present analytical results for the force between objects of various shapes and substrates, and between pairs of objects. We compare the results to those from more exact numerical calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings; the analytical PFA results together with the geometrical correction factors are summarized in a table.