1996
DOI: 10.1209/epl/i1996-00248-2
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Multifractality beyond the parabolic approximation: Deviations from the log-normal distribution at criticality in quantum Hall systems

Abstract: Based on differences of generalized Rényi 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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Cited by 11 publications
(10 citation statements)
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“…[23][24][25][26][27] Now, let us proceed with the shape analysis of the P (s) function using the other two quantities q and S str . As it has been shown in a number of cases 20,22) As we can see our data indicate a similar behavior as the random-Landau matrix model. This is another nice example of the presence of one-parameter scaling since all data can be described by a one-parameter family of P (s) functions.…”
supporting
confidence: 88%
See 1 more Smart Citation
“…[23][24][25][26][27] Now, let us proceed with the shape analysis of the P (s) function using the other two quantities q and S str . As it has been shown in a number of cases 20,22) As we can see our data indicate a similar behavior as the random-Landau matrix model. This is another nice example of the presence of one-parameter scaling since all data can be described by a one-parameter family of P (s) functions.…”
supporting
confidence: 88%
“…[23][24][25][26][27] Now, let us proceed with the shape analysis of the P (s) function using the other two quantities q and S str . As it has been shown in a number of cases 20,22) these parameters apart from showing scaling and fixed point in the critical regime, as a bonus enable us to determine the one-parameter family of P (s) functions describing the transition from e.g. GUE-like to Poissonian behavior.…”
mentioning
confidence: 99%
“…However, the figure clearly shows deviation from the log-normal form especially for the low-y part of the distribution that may be described with a power law tail of the form y 1.6 . Similar deviations have already been detected and studied at the quantum-Hall transition 26 and are clearly seen at the Anderson-transition in d = 3 systems 27 , as well. In summary we have investigated the spectral properties of a random matrix ensemble with entries decaying away from the diagonal in a power-law fashion.…”
supporting
confidence: 83%
“…However, as it has been demonstrated in Ref. 12 and applied in several studies later 12,13,14,15,16 , the difference…”
Section: Basic Ideasmentioning
confidence: 77%
“…A number of applications have been presented to date 13 showing their diverse applicability starting from quantum chemistry 14 up to localization in disordered and quasiperiodic systems 15 up to the statistical analysis of spectra 16 . In the present work we are going to extend this formalism to continuous distributions and show again that the differences of Rényi entropies are good candidates for the characterization of them.…”
Section: Basic Ideasmentioning
confidence: 99%