We demonstrate the level statistics in the vicinity of the Anderson transition in d>2 dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of the number of levels N in a given energy interval with 〈N〉≫1 is proved to behave as 〈N${\mathrm{〉}}^{\gamma }$ where γ=1-(νd${)}^{\mathrm{-}1}$ and ν is the correlation length exponent. The inequality γ<1, shown to be required by an exact sum rule, results from nontrivial cancellations (due to the causality and scaling requirements) in calculating the two-level correlation function.

• Received 20 September 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.888