Spectral rigidity and eigenfunction correlations at the Anderson transition
نویسندگان
چکیده
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 〈(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. Typeset using REVTEX
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