Christian Ferrari and Nicolas Macris
Extended energy levels for macroscopic Hall systems
(329K, Postscript)
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.