Abstract

Some aspects of anyon physics are reviewed with the intention of establishing a model for the quantization of the Hall conductance. A single particle Schrödinger model is introduced and coupled with a constraint equation formulated from the anyon picture. The Schrödinger equation-constraint system can be converted to a single nonlinear differential equation and solutions for the model can be produced.

Highlights

  • The quantum Hall effect is a recently discovered and well known phenomenon which appears in a twodimensional electron system which exhibits spectacular phenomena when subjected to an intense transverse magnetic field [1]

  • Some aspects of anyon physics are reviewed with the intention of establishing a model for the quantization of the Hall conductance

  • A single particle Schrödinger model is introduced and coupled with a constraint equation formulated from the anyon picture

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Summary

Introduction

The quantum Hall effect is a recently discovered and well known phenomenon which appears in a twodimensional electron system which exhibits spectacular phenomena when subjected to an intense transverse magnetic field [1]. First encountered experimentally [2], the integer quantum Hall effect has received much study, and was subsequently followed by the fractional Hall effect [3,4] Referring to these two effects as the quantum Hall effect, the Hall resistance is found experimentally to exhibit plateaus at the quantized values. The two effects show remarkable similarities despite the differences in origin In both effects, the localization of electrons and quasiparticles is believed to be responsible for the formation of the plateaus in the Hall conductivity. It is the intention here to set up and solve a simple version of (2) subject to a physical constraint. Let us proceed to this [5,6]

Setting up the Model-Composite Particles
Solution of the Schrödinger Equation
Conclusions
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