Multifractality beyond the Parabolic Approximation: Deviations from the Log-normal Distribution at Criticality in Quantum Hall Systems

Physics – Condensed Matter – Mesoscale and Nanoscale Physics

Scientific paper

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LaTeX 4 pages, 3 EPS included, to appear in Europhysics Letters

Scientific paper

10.1209/epl/i1996-00248-2

Based on differences of generalized R\'enyi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two--measure random Cantor set are calculated exactly and finally using the results of numerical simulations the distribution of the eigenvector components calculated in the critical region of the lowest Landau--band is analyzed.

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