Spectral rigidity and eigenfunction correlations at the Anderson transition
- 1 September 1996
- journal article
- Published by Pleiades Publishing Ltd in JETP Letters
- Vol. 64 (5) , 386-392
- https://doi.org/10.1134/1.567208
Abstract
The statistics of energy levels for a disordered conductor are considered in the critical energy window near the mobility edge. It is shown that, if the critical wave functions are multifractal, the one-dimensional gas of levels on the energy axis is compressible, in the sense that the variance of the level number in an interval is 〈 (δN)2〉∼χ〈N〉 for 〈N〉≫1. The compressibility, χ=η/2d, is given exactly in terms of the multifractal exponent η =d−D2 at the mobility edge in a d-dimensional system.Keywords
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