Mobility edges for the quantum percolation problem in two and three dimensions

Numerical results are reported for the quantum site-percolation problem. For the square lattice and the simple cubic lattice quantum percolation thresholds ${\mathit{p}}_{\mathit{q}}$ are calculated by studying the sensitivity of eigenvalues to a change in boundary conditions. Observing the energy dependence of the transition from localized to extended states, mobility edge trajectories are calculated. We obtain ${\mathit{p}}_{\mathit{q}}$=0.45 in three dimensions and ${\mathit{p}}_{\mathit{q}}$=0.70 in two dimensions. The latter value of ${\mathit{p}}_{\mathit{q}}$ is identified with a transition from weakly to strongly localized states, according to a similar localization behavior observed for the Anderson problem.