Roughness Dependence of the Casimir Force between Fractal Surfaces

Abstract

We study the surface-roughness dependence of the Casimir force between fractal surfaces, which is represented by the Weierstrass-Mandelbrot function. When compared the Casimir force in the case of smooth surfaces, the Casimir force between fractal surfaces rapidly increases as the separation distance decreases. We express this deviation as a simple analytical function that is composed of three parameters including fractal dimension, and compare it with the deviation obtained from Monte Carlo simulations. [DOI: 10.1380/ejssnt.2014.313]