Self-affine roughness influence on the Casimir effect

In this work we investigate the influence of self-affine roughness on the Casimir energy for plate-plate geometry. The plate roughness is characterized by the rms roughness amplitude w, the lateral correlation length ξ, and the roughness exponent H. It is shown that the latter has a prominent effect on the Casimir energy with respect to the long-wavelength roughness ratio w/ξ. Analytic results are shown for three characteristic roughness exponents, namely, H=0, 0.5, and 1. Moreover, the dynamic evolution of the surface roughness (e.g., by metal deposition) leads to significant contributions of the roughness influence on the Casimir energy.