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Abstract : Because of a mathematical analogy, the anomalous quantum Hall effect might be related to the classical statistical mechanics of a two-dimensional generalized plasma : this is a two-dimensional system of two species of particles, interacting through logarithmic potentials, with three independent coupling constants instead of two charges for an ordinary two-component plasma. Sum rules are derived for such systems. A one-dimensional solvable model is studied and shown to obey the one-dimensional analogs of the sum rules.

Keywords : Hall effect solid state plasma one dimensional model Landau level two dimensional electron gas anomalous quantum Hall effect classical statistical mechanics two dimensional generalized plasma logarithmic potentials coupling constants sum rules

Author: P.J. Forrester B. Jancovici



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