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Critical quantum chaos and the one-dimensional harper model
1Department of Physics, University of Ioannina, Ioannina 45 110, Greece.
Physical Review Letters
|September 20, 2011
Summary
We numerically found a scale-invariant bandwidth distribution for the critical Harper model, described by a semi-Poisson curve. This suggests universal critical spectral statistics and a link to multifractality.
Area of Science:
- Condensed matter physics
- Quantum chaos
- Disordered systems
Background:
- The critical Harper model is a key system for studying Anderson localization and quantum chaos.
- Understanding spectral statistics is crucial for characterizing quantum systems.
Purpose of the Study:
- To numerically obtain the bandwidth distribution for the critical Harper model.
- To investigate the universality of critical spectral statistics.
- To explore the connection between spectral properties and multifractality.
Main Methods:
- Numerical simulations of the critical Harper model.
- Analysis of bandwidth distributions.
- Spectral unfolding techniques.
- Deduction of level spacing distributions and number variance.
Main Results:
- A scale-invariant bandwidth distribution was obtained, closely matching a semi-Poisson curve P(S)=4Sexp(-2S).
- After spectral unfolding, a semi-Poisson level spacing distribution was deduced.
- A sub-Poisson linear number variance was derived from the bandwidth distribution.
Conclusions:
- The results support the universality of critical spectral statistics in the Harper model.
- A connection between spectral statistics and spectral multifractality is suggested.
- The findings contribute to the understanding of quantum chaos in disordered systems.
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