Level statistics and localization in a two-dimensional quantum percolationproblem

A two-dimensional model for quantum percolation with variable tunnelling ra nge is studied. For this purpose the Lifshitz distribution is considered wh ere the disorder enters the Hamiltonian via the non-diagonal hopping elemen ts. We employ a numerical method to analyse the level statistics of this mo del. It turns out that the level repulsion is strongest around the percolat ion threshold. As we go away from the maximum level repulsion a cross-over from a Gaussian orthogonal ensemble type of behaviour to a Poisson-like dis tribution is revealed. The localization properties are calculated by using the sensitivity to boundary conditions and we find a cross-over from locali zed to delocalized states.