Parametric models of the Hall effect in the strongly correlated regime

Abstract

I examine a nonlinear model of the Hall effect in the strongly correlated regime. The model entails the magnetic Schrödinger equation supplemented with a strongly nonlinear charge-to-field-to-charge feedback loop. This structure is related to, but distinct from, the mesoscopic loop models of systems in the quantum Hall regime. The introduction of the specific type of nonlinearity in the model at hand leads to a break-down of the symmetries displayed by the familiar linear problem. In particular, the model predicts a Hall potential with either regular or anomalous bias and, simultaneously, the formation of stable charge-stripes. Our motivation for the study of constructive PDE-based models of quantum phenomena is largely motivated by applications to nanosystem specific signal processing. Indeed, models such as these enable the construction of statistical parameter spaces adapted to the specificity of signals generated by the systems they describe.