Quantum percolation in three-dimensional systems.

The quantum site- and bond-percolation problems, which are defined by a disordered tight-binding Hamiltonian with a binary probability distribution, are studied using finite-size scaling methods. For the simple-cubic lattice, the dependence of the mobility edge on the strength of the disorder is obtained for both the site- and bond-percolation case. We find that the quantum percolation threshold is {ital p}{sub {ital q}}{sup {ital s}}=0.44{plus minus}0.01 for the site case and {ital p}{sub {ital q}}{sup {ital b}}=0.32{plus minus}0.01 for the bond case. A detailed numerical study of the density of states (DOS) is also presented. A rich structure in the DOS is obtained and its dependence on the concentration and strength of disorder is presented.