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The Level Spacing Distribution Near the Anderson Transition

Abstract

For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotics P(s)∝exp⁑(βˆ’As2βˆ’Ξ³)P(s)\propto \exp(-A s^{2-\gamma }) for s\gg \av{s}\equiv 1 which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson in an insulator. (Here the critical exponent 0<Ξ³<10<\gamma<1 and the numerical coefficient AA depend only on the dimensionality d>2d>2). It is obtained by mapping the energy level distribution to the Gibbs distribution for a classical one-dimensional gas with a pairwise interaction. The interaction, consistent with the universal asymptotics of the two-level correlation function found previously, is proved to be the power-law repulsion with the exponent βˆ’Ξ³-\gamma.Comment: REVTeX, 8 pages, no figure

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