Journal article
Extreme statistics of complex random and quantum chaotic states
Physical review letters, Vol.100(4), pp.044103-044103
2008
Handle:
https://hdl.handle.net/2376/113421
PMID: 18352278
Abstract
An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although the components are correlated by the normalization constraint, it is still possible to derive compact formulae for all values of the dimensionality N. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulae.
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Details
- Title
- Extreme statistics of complex random and quantum chaotic states
- Creators
- Arul Lakshminarayan - Max-Planck-Institut für Physik komplexer SystemeSteven Tomsovic - Max-Planck-Institut für Physik komplexer SystemeOriol Bohigas - Laboratoire de Physique Théorique et Modèles StatistiquesSatya N Majumdar - Laboratoire de Physique Théorique et Modèles Statistiques
- Publication Details
- Physical review letters, Vol.100(4), pp.044103-044103
- Academic Unit
- Physics and Astronomy, Department of
- Publisher
- American Physical Society
- Identifiers
- 99900548009301842
- Language
- English
- Resource Type
- Journal article