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 to search for universal principles relevant tonanosystem modeling and nanosystem-specific signal processing. Recently, we have been ableto construct a partial differential equations-based model of a quantum Hall system, whichconsists of the Schrödinger equation supplemented with a special-type nonlinear feedbackloop. This result stems from a novel theoretical approach, which in particular brings tothe fore the notion of quantum information. Here we undertake to modify the original model bysubstituting the dynamics based on the Dirac operator. This leads to a model that consistsof a system of three nonlinearly coupled first-order elliptic equations in the plane