1994/10/18 by J. M. Combes, Combes, J. M., Peter D. Hislop +2
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics #funct-an #math-ph #math.FA #math.MP
paper · pdf · doi:10.48550/arxiv.funct-an/9410005
34 pages,CPT-94/P.3061,LaTex
arxiv created 1994/10/18 · openalex publication_date 1994/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.