Level Spacing Distribution Near the Anderson Transition

AG Aronov, VE Kravtsov, Igor Lerner

Research output: Contribution to journalArticle


For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotic behavior P(s) proportional to exp(-As-2-gamma) for s much greater than [s] = 1, 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 <gamma <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 -gamma.
Original languageEnglish
Pages (from-to)39-44
Number of pages6
JournalJournal of Experimental and Theoretical Physics Letters
Issue number1
Publication statusPublished - 10 Jan 1994


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