Quantum Hydrodynamics of Fractional Hall Effect: Quantum Kirchhoff Equations

TL;DR

This paper develops a quantum hydrodynamics framework for fractional quantum Hall states by quantizing Kirchhoff equations, capturing key phenomena like Lorentz shear, magneto-roton spectrum, and Hall currents.

Contribution

It introduces a novel quantum hydrodynamics approach based on quantized Kirchhoff equations to describe FQH states comprehensively.

Findings

Captures Lorentz shear effects in FQH states

Describes magneto-roton spectrum accurately

Models Hall current in non-uniform fields

Abstract

We argue that flows of the quantum electronic liquid in the Fractional Quantum Hall state are comprehensively described by the hydrodynamics of vortices in the quantum incompressible rotating liquid. We obtain the quantum hydrodynamics of vortex flow by quantizing Kirchhoff equations for vortex dynamics. We demonstrate that quantized Kirchhoff equations capture all major features of FQH states including subtle effects of Lorentz shear force, magneto-roton spectrum, Hall current in a non-uniform electromagnetic field, thus providing a powerful framework to study FQHE and superfluids. The results are also useful for classical vortex flows.