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VOLUME 64 (1996) | ISSUE 5 | PAGE 355
Spectral rigidity and eigenfunction correlations at the Anderson transition
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 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 {(SN)1) ~ χ(Ν) for (N) > 1. The compressibility, χ r;/2d, is given exactly in terms of the multifractal exponent -η ™ d — D2 at the mobility edge in a d-dimensional system. PACS: 05.45+Ъ, 71.25.-s. 72.15,Rn.