Universal statistics of wave functions in chaotic and disordered systems
Abstract
We study a new statistics of wave functions in several chaotic and disordered systems: the random matrix model, band random matrix model, the Lipkin model, chaotic quantum billiard and the 1D tight-binding model. Both numerical and analytical results show that the distribution function of a generalized Riccati variable, defined as the ratio of components of eigenfunctions on basis states coupled by perturbation, is universal, and has the form of Lorentzian distribution.
- Publication:
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arXiv e-prints
- Pub Date:
- July 1998
- DOI:
- 10.48550/arXiv.chao-dyn/9807006
- arXiv:
- arXiv:chao-dyn/9807006
- Bibcode:
- 1998chao.dyn..7006H
- Keywords:
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- Chaotic Dynamics;
- Condensed Matter;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 6 Europhys pages, 2 Ps figures, new version to appear in Europhys. Lett