Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada
Copyright © 2009 Artur Sowa. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Quantum Hall systems are a suitable theme for a case study in the general area of nanotechnology.
In particular, it is a good framework to search for universal principles relevant to
nanosystem modeling and nanosystem-specific signal processing. Recently, we have been able
to construct a partial differential equations-based model of a quantum Hall system, which
consists of the Schrödinger equation supplemented with a special-type nonlinear feedback
loop. This result stems from a novel theoretical approach, which in particular brings to
the fore the notion of quantum information. Here we undertake to modify the original model by
substituting the dynamics based on the Dirac operator. This leads to a model that consists
of a system of three nonlinearly coupled first-order elliptic equations in the plane.