Spectral Statistics at the Anderson Transition: Multifractality of Wave Functions and the Violation of the Normalization Sum Rule

1996/03/26 by V. E. Kravtsov, Kravtsov, V. E.
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #cond-mat

paper · pdf · doi:10.48550/arxiv.cond-mat/9603166

Proceedings of the Correlated Fermions and Transport in Mesoscopic Systems Moriond Conference, Les Arcs, 1996. 10 pages REVTEX, one figure

arxiv created 1996/03/26 · arxiv updated 2009/11/30

Abstract

The statistics of energy levels of electrons in a random potential is considered in the critical energy window near the mobility edge. It is shown that the multifractality of critical wave functions results in the violation of the normalization sum rule in the thermodynamic limit and leads to the quasi-Poisson linear term in the level number variance. The slope of the linear term is equal to the sum rule deficiency which is expressed in terms of the fractal dimension D(2).

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