The fractional quantum Hall effect.

Quantum Hall Dynamics on Von Neumann Lattice

h in quantum Hall regime of the system of interactions and disorders. This shows that a determination of the fine structure constant from integer quantum Hall effect is in fact possible. We present also a unified mean field theory of the fractional Hall effect for the in-compressible quantum liquid states based on flux condensation and point out that the known Hofstadter butterfly spectrum of t...

Observation of the fractional quantum Hall effect in GaAs-(Ga,A1)As quantum well structures

Twisted Index Theory on Orbifold Symmetric Products and the Fractional Quantum Hall Effect

We extend the noncommutative geometry model of the fractional quantum Hall effect, previously developed by Mathai and the first author, to orbifold symmetric products. It retains the same properties of quantization of the Hall conductance at integer multiples of the fractional Satake orbifold Euler characteristics. We show that it also allows for interesting composite fermions and anyon represe...

J un 1 99 7 Exclusonic Quasiparticles and Thermodynamics of Fractional Quantum Hall Liquids

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving different assumptions on statistical correlations. Thermal activation of quasiparticle pairs and thermodynamic properties of the fractional quantum Hall liquids ne...

Is There Another Scale in the Fractional Quantum Hall Effect?

We reanalyse theoretical considerations and experimental data, in an attempt to decide whether there is another scale in the fractional quantum Hall effect problem, in addition to the magnetic scale defined by the magnetic length a c or the cyclotron energy ¯ hω c. We then discuss possible implications of a new scale on the formulation of a theoretical model of the fractional quantum Hall effect.

Higher Order Addition Laws on Abelian Varieties and the Fractional Quantum Hall Effect

Addition formulas for theta functions of arbitrary order are shown and applied to the theoretical understanding of the fractional quantum Hall effect in a multi-layer two-dimensional many-electron system under periodic conditions.