On the effective hydrodynamics of FQHE

TL;DR

This paper develops a classical hydrodynamic model that captures key properties of the Fractional Quantum Hall effect, including Hall viscosity and conductivity, and relates to established quantum theories.

Contribution

It introduces a classical fluid model with FQHE-like properties and connects it to the Chern-Simons-Ginzburg-Landau theory and Laughlin's wave function.

Findings

Model reproduces Hall viscosity and conductivity.

Shows relation to Chern-Simons-Ginzburg-Landau theory.

Laughlin's wave function is annihilated by the quantum velocity operator.

Abstract

We present here a classical hydrodynamic model of a two-dimensional fluid which has many properties of Fractional Quantum Hall effect. This model incorporates the FQHE relation between the vorticity and density of the fluid and exhibits the Hall viscosity and Hall conductivity found in FQHE liquids. We describe the relation of the model to the Chern-Simons-Ginzburg-Landau theory of FQHE and show how Laughlin's wave function is annihilated by the quantum velocity operator.