What is it about?
A charge-conducting 2D plate and a transversal magnetic field are viewed as a composite quantum system. With some assumptions this leads to a system of PDEs that predicts quantization of the Hall resistance. In such (effective) models the magnetic field density is spatially variable. In a previous article (cited in the present one) the electronic transport was modeled via the Schrodinger equation. In the present work it is modeled via the Dirac equation.
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Why is it important?
It is a nontrivial matter to obtain a PDE model of the Quantum Hall Effect. Such models enable a direct investigation of the vulnerability of the QHE to perturbing potential and/or disorder.
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This page is a summary of: Modeling a Quantum Hall System via Elliptic Equations, Advances in Mathematical Physics, January 2009, Hindawi Publishing Corporation,
DOI: 10.1155/2009/514081.
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