Christian Ferrari, Nicolas Macris
Spectral Properties of Finite Quantum Hall Systems
(192K, Postscript)

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).