Landau Hamiltonians with random potentials: Localization and the density of states

J. M. Combes, P. D. Hislop

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding eigenfunctions decay exponentially with the magnetic field and distance. We also prove that the integrated density of states is Lipschitz continuous away from the Landau energies. The proof relies on a Wegner estimate for the finite-area magnetic Hamiltonians with random potentials and exponential decay estimates for the finite-area Green's functions. The proof of the decay estimates for the Green's functions uses fundamental results from two-dimensional bond percolation theory.

Original languageEnglish
Pages (from-to)603-629
Number of pages27
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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