Parametric invariant Random Matrix Model and the emergence of multifractality
arXiv:cond-mat/0508497 · doi:10.1103/PhysRevE.73.036204
Abstract
We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the non-perturbative crossover that has been discussed by Wigner 50 years ago. Of particular interest is the emergence of an additional crossover to multifractality.
7 pages, 6 figures, expanded version
References in corpus (7)
- Probing the eigenfunction fractality with a stop watch
- A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
- Fluctuations of wave functions about their classical average
- From Chaos to Disorder in Quasi-1D Billiards with Corrugated Surfaces
- Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces
- Orbital magnetic properties of quantum dots: the role of electron-electron interactions
- The twilight zone in the parametric evolution of eigenstates: beyond perturbation theory and semiclassics
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- Scattering and transport statistics at criticality
- Quantum anomalies and linear response theory