Abstract
In this paper, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed by a random alloy-type potential constructed with single-site potentials decaying at least at a Gaussian speed. We prove that, if the Landau level stays preserved as a band edge for the perturbed Hamiltonian, at the Landau levels, the integrated density of states has a Lifshitz behavior of the type .RésuméDans cette note, nous démontrons qu'en dimension 2, la densité d'états intégrée d'un opérateur de Landau avec un potentiel aléatoire non négatif de type Anderson dont le potentiel de simple site décroît au moins aussi vite qu'une fonction gaussienne admet en chaque niveau de Landau, disons, 2bq, si celui-ci est un bord du spectre, une asymptotique de Lifshitz du type .
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More From: Journal of Physics A: Mathematical and Theoretical
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