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Advances in Mathematical Physics
Volume 2009, Article ID 514081, 9 pages
Research Article

Modeling a Quantum Hall System via Elliptic Equations

Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, Canada S7N 5E6

Received 19 June 2008; Revised 22 August 2008; Accepted 8 September 2008

Academic Editor: Shao-Ming Fei

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.