The level spacing distribution near the Anderson transition
Aronov A.G., Kravtsov V.E., Lerner I.V.
For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotics P(») oc exp(-As2""*) fcr *><*) = 1 which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson in an insulator. (Here the critical exponent 0 < 7 < 1 *n<* the numerical coefficient A depend only on the dimensionality d > 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 -7.
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![](/ps/316/article_5028_800_head.png "<b>For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotics <i>P(») </i>oc <i>exp(-As<sup>2</sup>""*) </i>fcr *><*) = </b><b>1 </b><b>which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson in an insulator. (Here the critical exponent </b><b>0 < 7 < 1 </b><b>*n<* the numerical coefficient A depend only on the dimensionality <i>d </i></b><b>> 2). </b><b>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 </b><b>-7.</b>")