Roughness correction to the Casimir force beyond perturbation theory

TL;DR

This paper introduces a new method to accurately calculate the Casimir force considering surface roughness, especially when roughness peaks are comparable to the separation distance, improving predictions at short ranges.

Contribution

It develops a novel approach combining extreme value statistics and perturbative methods to account for high peaks and normal roughness in Casimir force calculations.

Findings

The method accurately predicts deviations from Casimir scaling at short separations.

High peaks can be treated independently in force calculations.

The approach explains previously unexplained experimental deviations.

Abstract

Up to now there has been no reliable method to calculate the Casimir force when surface roughness becomes comparable with the separation between bodies. Statistical analysis of rough Au films demonstrates rare peaks with heights considerably larger than the root-mean-square (rms) roughness. These peaks define the minimal distance between rough surfaces and can be described with extreme value statistics. We show that the contributions of high peaks to the force can be calculated independently of each other while the contribution of normal roughness can be evaluated perturbatively beyond the proximity force approximation. The developed method allows a reliable force estimation for short separations. Our model explains the strong hitherto unexplained deviation from the normal Casimir scaling observed experimentally at short separations.