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 var...
| Main Authors: | , , |
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| Format: | Journal article |
| Published: |
1996
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| Summary: | 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.</n></n> |
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