02-255 Christian Ferrari and Nicolas Macris

Extended energy levels for macroscopic Hall systems (329K, Postscript) Jun 6, 02

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Abstract. We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is L-periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. We prove that, with large probability, in a subset of the first gap of the pure bulk Hamiltonian the spectrum of the full Hamiltonian consists only on eigenenergies whose eigenfuntions are extended, in the sense that their quantum mechanical currents are strictly positive/negative with respect to the size of the system.

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