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  • 1
    ISSN: 1572-9613
    Keywords: Quantum Hall effect ; classification of universality classes of quantum Hall fluids ; integral lattices ; quadratic forms ; lattice embeddings ; phase transitions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper, the key ideas of characterizing universality classes of dissipationfree (incompressible) quantum Hall fluids by mathematical objects called quantum Hall lattices are reviewed. Many general theorems about the classification of quantum Hall lattices are stated and their physical implications are discussed. Physically relevant subclasses of quantum Hall lattices are defined and completely classified. The results are carefully compared with experimental data and also with other theoretical schemes (the hierarchy schemes). Several proposals for new experiments are made which could help to settle interesting issues in the theory of the (fractional) quantum Hall effect and thus would lead to a deeper understanding of this remarkable effect.
    Type of Medium: Electronic Resource
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