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Quantum Hall systems are a suitable theme for a case study in the generalarea of nanotechnology. In particular, it is a good framework in which tosearch for universal principles relevant to nanosystem modeling, andnanosystem-specific signal processing. Recently, we have been able to constructa PDE model of a quantum Hall system, which consists of the Schr\"odingerequation supplemented with a special type nonlinear feedback loop. This resultstems from a novel theoretical approach, which in particular brings to the forethe notion of quantum information. In this article we undertake to modify theoriginal model by substituting the dynamics based on the Dirac operator. Thisleads to a model that consists of a system of three nonlinearly coupled firstorder elliptic equations in the plane.

Modeling a quantum Hall system via elliptic equations