The effect of roughness and correlation on the Casimir torque between two plates

Abstract

The effect of roughness and correlation on the Casimir torque is studied. The plates are assumed to be perfect conductors. This is a good approximation when the separation between plates is not too small. The pairwise summation (PWS) method is used, which is a good approximation when the correlation length is much larger than the distance between the plates. Torque components both parallel and perpendicular to the plates are obtained. It is seen that the component parallel to the plates is nonvanishing even if the plates are smooth, but there are contributions due to roughness and correlation as well, and the contribution of the correlation is an increasing function of both the roughness exponent and the correlation length. The component perpendicular to the plates, however, is nonvanishing only if the plates are rough and correlated to each other. As the roughness exponent increases, this component increases, reaches a peak and then decreases.