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) pr oportional to exp(-As-2-gamma) for s much greater than [s] = 1, which is universal and intermediate between the Gaussian asymptotics in a me tal and the Poisson asymptotics in an insulator. (Here the critical ex ponent is in the range 0 < gamma < 1, and the numerical coefficient A depends only on the dimensionality d > 2.) It is obtained by mapping t he energy level distribution onto the Gibbs distribution for a classic al one-dimensional gas with a pairwise interaction. The interaction, w hich is consistent with the universal asymptotic behavior of the two-l evel correlation function found previously, was found to be the power- law repulsion with the exponent -gamma.