Multifractality and critical fluctuations at the Anderson transition

Abstract

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.

14 pages, 13 eps figures

References in corpus (6)

• Statistics of energy levels and eigenfunctions in disordered systems
• Fluctuations of the inverse participation ratio at the Anderson transition
• Towards a Field Theory of the Plateau Transition
• Critical Hamiltonians with long range hopping
• Critical statistics in a power-law random banded matrix ensemble
• Distribution of fractal dimensions at the Anderson transition

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