Multifractality and critical fluctuations at the Anderson transition

Details Multifractality and critical fluctuations at the Anderson transition Multifractality and critical fluctuations at the Anderson transition

2000-03-20

arxiv.org/abs/cond-mat/0003332v1

Phys. Rev. B 62, 7920 (2000).

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

14 pages, 13 eps figures

Scientific paper

10.1103/PhysRevB.62.7920

Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse participation ratios (IPR) $P_q$ are scale-invariant at the critical point, with a power-law asymptotic tail. The IPR distribution, the multifractal spectrum and the level statistics are calculated analytically in the limits of weak and strong couplings, as well as numerically in the full range of couplings.

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