Dispersion Law of Edge Waves in the Quantum Hall Effect

Details Dispersion Law of Edge Waves in the Quantum Hall Effect Dispersion Law of Edge Waves in the Quantum Hall Effect

1993-11-25

arxiv.org/abs/cond-mat/9311057v1

Physics

Condensed Matter

10 pages, 2 figures upon request, UTF-311-11/93

Scientific paper

10.1103/PhysRevLett.72.3230

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.

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