Fluctuations of the inverse participation ratio at the Anderson transition

Details Fluctuations of the inverse participation ratio at the Anderson transition Fluctuations of the inverse participation ratio at the Anderson transition

2000-01-08

arxiv.org/abs/cond-mat/0001086v1

Phys. Rev. Lett. 84, 3690 (2000).

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 3 eps figures

Scientific paper

10.1103/PhysRevLett.84.3690

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 $D_q$ are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between $D_2$ and the spectral compressibility $\chi$ is violated in the regime of strong multifractality, with $\chi\to 1$ in the limit $D_2\to 0$.

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