96-307 Barbaroux J.M., Combes J.M., Hislop P.D.

Landau hamiltonians with unbounded random potentials (47K, LaTeX) Jun 18, 96

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Abstract. We prove the almost sure existence of pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. We also prove that the integrated density of states is Lipschitz continuous away from the Landau energies $E_n(B)$. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding density $g$ has support equal to $\R$, and satisfies $\mbox{sup}_{\lambda \in \R} \{ \lambda^{ 3 + \epsilon } g ( \lambda ) \} < \infty $, for some $\epsilon > 0$.

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