Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition

Details Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition

1996-09-04

arxiv.org/abs/cond-mat/9609039v1

JETP Lett. 64 (1996) 386

Physics

Condensed Matter

10 pages in REVTeX preprint format; to be published in JETP Letters, 1996

Scientific paper

10.1134/1.567208

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 $< (\delta N)^{2} > = \chi $ for $ >> 1$. The compressibility, $\chi=\eta/2d$, is given ``exactly'' in terms of the multifractal exponent $\eta=d-D_2$ at the mobility edge in a $d$-dimensional system.

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