 02121 Christian Ferrari, Nicolas Macris
 Spectral Properties of Finite Quantum Hall Systems
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Mar 14, 02

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Abstract. In this note we review spectral properties of magnetic random Schroedinger
operators H_omega=H_0+V_omega + U_l + U_r defined on L^2(IR x [L/2,L/2])
with periodic boundary conditions along y. U_l and U_r are two confining
potentials for x<L/2 and x>L/2 respectively and vanish for L/2<x<L/2.
We describe the spectrum in two energy intervals and we classify it according
to the quantum mechanical current of eigenstates along the periodic direction.
The first interval lies in the first Landau band of the bulk Hamiltonian,
and contains intermixed eigenvalues with a quantum mechanical current of
O(1) and O(e^{cB(log L)^2}) respectively. The second interval lies in
the first spectral gap of the bulk Hamiltonian, and contains only eigenvalues
with a quantum mechanical current of O(1).
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