Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition

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 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 $<(\delta N{)}^2>=\chi <N>$ for $<N>>>1$. 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.

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

References in corpus (1)

• Random Walks through the Ensemble: Linking Spectral Statistics with Wavefunction Correlations in Disordered Metals

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