Effects of dielectric disorder on van der Waals interactions in slab geometries

We analyze the effects of disorder on the thermal Casimir interaction for the case of two semi-infinite planar slabs across an intervening homogeneous unstructured dielectric. The semi-infinite bounding layers are assumed to be composed of plane-parallel layers of random dielectric materials. We show that the effective thermal Casimir interaction at long distances is self-averaging and can be written in the same form as the one between nonrandom media but with the effective dielectric tensor of the corresponding random media. On the contrary, the behavior at short distances becomes random, and thus sample dependent, dominated by the local values of the dielectric constants proximal to each other across the central homogeneous unstructured dielectric layer. We extend these results to the regime of intermediate slab separations by using perturbation theory for weak disorder as well as by extensive numerical simulations for a number of systems where the dielectric function has a log-normal distribution. Numerical simulation completely corroborates all the main features of the disorder dependent thermal Casimir interaction deduced analytically.