02-172 J.-M. Combes, P. D. Hislop, E. Soccorsi

Edge states for quantum Hall Hamiltonians (232K, Postscript) Apr 6, 02

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Abstract. The study of the quantum motion of a charged particle in a half-plane as well as in an infinite strip submitted to a perpendicular constant magnetic field $B$ reveals eigenstates propagating permanently along the edge, the so-called edge states. Moreover, in the half-plane geometry, current carried by edge states with energy in between the Landau levels persists in the presence of a perturbing potential small relative to B. We show here that edge states carrying current survive in an infinite strip for a long time before tunneling between the two edges has a destructive effect on it. The proof relies on Helffer-Sj\"ostrand functional calculus and decay properties of quantum Hall Hamiltonian resolvent.

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