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VOLUME 59 (1994) | ISSUE 1 | PAGE 40
Level spacing distribution near the Anderson transition
For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotic behavior P(s) <χ exp( — /Is2"7) for s>(i)sl, which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson asymptotics in an insulator. (Here the critical exponent is in the range 0<γ< 1, and the numerical coefficient A depends only on the dimensionality d>2.) It is obtained by mapping the energy level distribution onto the Gibbs distribution for a classical one-dimensional gas with a pairwise interaction. The interaction, which is consistent with the universal asymptotic behavior of the two-level correlation function found previously, was found to be the power-law repulsion with the exponent —γ.