Spectral Properties of Finite Quantum Hall Systems ∗

In this note we review spectral properties of magnetic random Schrödinger operators Hω = H0 + Vω + Ul + Ur defined on L 2(R × [ −L2 , L2 ] , dxdy) with periodic boundary conditions along y. Ul and Ur are two confining potentials for x ≤ −L2 and x ≥ L2 respectively and vanish for −L2 ≤ x ≤ L2 . 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 (