A NEW MODEL OF QUANTUM CHAOTIC BILLIARDS - APPLICATION TO GRANULAR METALS

We discuss the properties of a recently proposed model of quantum chao tic billiards in two and three dimensions. The model is based on a tig ht-binding Hamiltonian in which the energies of the atomic levels at t he boundary sites are chosen at random between -W/2 and W/2. The energ y spectra show a complex behavior with regions that obey Wigner-Dyson statistics, and regions with localized and quasi-ideal states distribu ted according to Poisson statistics. Whereas at low energies long-rang e energy fluctuations follow Random Matrix Theory (RMT) for all W, at high energies fluctuations are below (above) RMT for small (large) W. For small W, the mean free path I is proportional to L/W-2, L being th e system size, and reaches a minimum for W of the order of the band wi dth, at which I approximate to L/2. In 3D we found that the energy flu ctuations of the highest occupied level are much larger than the avera ge interlevel spacing. This provides an explanation for autoionization effects of the grains in granular metals.