Peter D. Hislop, Eric Soccorsi
Edge Currents for Quantum Hall Systems, II. Two-Edge, Bounded and Unbounded Geometries
(126K, Latex 2e)
ABSTRACT. Devices exhibiting the integer quantum Hall effect can be modeled
by one-electron Schroedinger operators describing the planar motion of an
electron in a perpendicular, constant magnetic field, and under the
influence of an electrostatic
potential. The electron motion is confined to bounded or
unbounded subsets of the
plane by confining potential barriers. The edges of the confining potential
barriers create edge currents.
This is the second of two papers in which we review recent progress
and prove explicit lower
bounds on the edge currents associated with one- and two-edge
geometries. In this paper, we study various
unbounded and bounded, two-edge
geometries with soft and hard confining potentials.
These two-edge geometries describe the electron confined to unbounded
regions in the plane, such as a strip, or to
bounded regions, such as a finite length cylinder.
We prove that the edge currents are stable under various
perturbations, provided they are suitably small relative to the magnetic
field strength, including perturbations by random potentials.
The existence of, and
the estimates on, the edge currents are independent of the spectral type of
the operator.