773 research outputs found
Fluctuations of the inverse participation ratio at the Anderson transition
Statistics of the inverse participation ratio (IPR) at the critical point of
the localization transition is studied numerically for the power-law random
banded matrix model. It is shown that the IPR distribution function is
scale-invariant, with a power-law asymptotic ``tail''. This scale invariance
implies that the fractal dimensions are non-fluctuating quantities,
contrary to a recent claim in the literature. A recently proposed relation
between and the spectral compressibility is violated in the regime
of strong multifractality, with in the limit .Comment: 4 pages, 3 eps figure
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