Quantum percolation and the Anderson transition in dilute systems

Computer-simulation results are presented for quantum systems with discrete off-diagonal disorder in square and cubic lattices. For the quantum percolation model with bonds present or absent at random the density of states shows a dip at the band center which develops into a gap for strong dilution. The relation between the quantum and geometrical percolation thresholds $p_q>p_e$ is satisfied for these lattices as well as for Cayley trees. In a model with alternating sign of bonds, most of the states in the band remain delocalized.