THE NATURE OF THE SPECTRUM FOR A LANDAU HAMILTONIAN WITH DELTA-IMPURITIES

We consider a single-band approximation to the random Schrodinger oper ator in an external magnetic field. The random potential consists of d elta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the entire spectrum of this H amiltonian when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level in the absence of a random potential being infinitely de generate, while the eigenfunctions corresponding to energies in the re st of the spectrum are localized.