  Quantum chaotic dynamics is obtained for a tight-binding model in which the
energies of the atomic levels at the boundary sites are chosen at random.
Results for the square lattice indicate that the energy spectrum shows a
complex behavior with regions that obey the Wigner-Dyson statistics and
localized and quasi-ideal states distributed according to Poisson statistics.
Although the averaged spatial extension of the eigenstates in the present model
scales with the size of the system as in the Gaussian Orthogonal Ensemble, the
fluctuations are much larger.
