Mean free path and energy fluctuations in quantum chaotic billiards

The elastic mean free path of carriers in a recently introduced model of quantum chaotic billiards in two and three dimensions is calculated The model incorporates surface roughness at a microscopic scale by randomly choosing the atomic levels at the surface sites between -W/2 and W/2. Surface roughness yields a mean free path l that decreases as L/W-2 as W increases, L being the linear system size. But this diminution ceases when the surface layer begins to decouple from the bulk for large enough values of W, leaving more or less unperturbed states on the bulk. Consequently, the mean free path shows a minimum of about L/2 for W of the order of the bandwidth. Energy fluctuations reflect the behavior of the mean free path. At small energy scales, strong level correlations manifest themselves by small values of Sigma(2)(E) that are close to random matrix theory (RMT) in all cases. At larger energy scales, fluctuations are below the logarithmic behavior of RMT for l>L, and above RMT value when l<L.