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Signatures of prelocalized states in classically chaotic systems
A Ossipov1, Tsampikos Kottos, T Geisel
1Max-Planck-Institut für Strömungsforschung und Fakultät Physik der Universität Göttingen, Bunsenstrasse 10, D-37073 Göttingen, Germany.
Summary
We studied eigenfunction intensity statistics in chaotic diffusion systems. Our findings challenge some theories and align with nonlinear sigma model predictions for 2D systems.
Area of Science:
- Quantum chaos
- Statistical mechanics
- Condensed matter physics
Background:
- Eigenfunction intensity statistics are crucial for understanding quantum chaos.
- Previous theoretical work has proposed different frameworks for analyzing these statistics in disordered systems.
Purpose of the Study:
- To investigate the statistical distribution of eigenfunction intensities (P(/psi/(2))) in dynamical systems exhibiting classical chaotic diffusion.
- To compare these statistics against existing theoretical predictions, specifically the optimal fluctuation method and the nonlinear sigma model.
Main Methods:
- Analysis of eigenfunction intensity distributions in systems with chaotic diffusion.
- Comparison of empirical results with theoretical models, including the optimal fluctuation method and the nonlinear sigma model.
Main Results:
- The study found that the tails of the eigenfunction intensity distribution P(/psi/(2)) in 2D systems contradict the optimal fluctuation method.
- Conversely, the results show strong agreement with predictions from the nonlinear sigma model.
Conclusions:
- The findings challenge the applicability of certain field theoretical predictions in the context of diffusive disordered samples.
- The nonlinear sigma model provides a more accurate description of eigenfunction intensity statistics in these chaotic systems.