Modeling a quantum Hall system via elliptic equations

Quantum Hall systems are a suitable theme for a case study in the general area of nanotechnology. In particular, it is a good framework in which to search for universal principles relevant to nanosystem modeling, and nanosystem-specific signal processing. Recently, we have been able to construct a PDE model of a quantum Hall system, which consists of the Schr\"odinger 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. In this article 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.