Noncommuting coordinates in the Hall effect and in vortex dynamics

TL;DR

This paper explores the connection between noncommuting coordinates in the quantum Hall effect and vortex dynamics, deriving Laughlin's Ansatz via exotic Galilei group extensions and linking it to fluid vortex models.

Contribution

It introduces a novel derivation of Laughlin's Ansatz using exotic Galilei group extensions, connecting quantum Hall physics with vortex dynamics in fluids.

Findings

Derived Laughlin's Ansatz from exotic Galilei group coupling

Linked fractional quantum Hall effect to vortex dynamics

Established equivalence between reduced systems and vortex models

Abstract

Laughlin's Ansatz to explain the fractional Quantum Hall effect is derived by coupling a particle associated with ``exotic'' the two-fold central extension of the planar Galilei group. The reduced system is identical to the one used to describe the dynamics of vortices in an incompressible planar fluid.