Complex dynamics of the integer quantum Hall effect
Abstract
We investigate both classical and quantum potential scattering in two dimensions in a magnetic field, with applications to the integer quantum Hall effect. Classical scattering is complex, due in one case to the approach of scattering states to an infinite number of bound states. We show that bound states are generic, and occur for all but extremely smooth scattering potentials. Quantum scattering follows the classical behavior rather closely, exhibiting sharp resonances rather than classical bound states. Extended scatterers provide an explanation for the breakdown of the QHE at a comparatively small Hall voltage.
 Publication:

Presented at the Physical Phenomena At High Magnetic Fields
 Pub Date:
 1991
 Bibcode:
 1991pphm.rept...15T
 Keywords:

 Hall Effect;
 Magnetic Effects;
 Magnetic Fields;
 Quantum Mechanics;
 Elastic Scattering;
 Hamiltonian Functions;
 Thermodynamics and Statistical Physics