Thermal Casimir effect between random layered dielectrics

We study the thermal Casimir effect between two thick slabs composed of plane-parallel layers of random dielectric materials interacting across an intervening homogeneous dielectric. It is found that the effective interaction at long distances is self-averaging and is given by a description in terms of effective dielectric functions. The behavior at short distances becomes random (sample dependent) and is dominated by the local values of the dielectric function proximal to each other across the dielectrically homogeneous slab.

Figure 1

(Color online) A schematic presentation of the model. Two finite slabs, (1) and (2), with disordered plane-parallel dielectric layers interacting across a dielectrically homogeneous slab of thickness $\ell$. $z$ axis is perpendicular to the plane of the slabs.