Dispersion Law of Edge Waves in the Quantum Hall Effect

TL;DR

This paper provides a microscopic and hydrodynamic analysis of edge wave dispersion in the quantum Hall effect, deriving explicit formulas and confirming them with numerical results, revealing different behaviors based on interaction range.

Contribution

It introduces a microscopic description of edge excitations in the quantum Hall effect and derives explicit dispersion laws, including the large N limit and short-range interaction cases.

Findings

Dispersion law proportional to q log(1/q) in large N limit.

Energy behaves as q^3 for short-range interactions.

Excellent agreement with numerical diagonalization results.

Abstract

We present a microscopic description of edge excitations in the quantum Hall effect which is analogous to Feynman's theory of superfluids. Analytic expressions for the excitation energies are derived in finite dots. Our predictions are in excellent agreement with the results of a recent numerical diagonalization. In the large $N$ limit the dispersion law is proportional to $qlog{1\over q}$. For short range interactions the energy instead behaves as $q^3$. The same results are also derived using hydrodynamic theory of incompressible liquids.