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Updated: Aug 9, 2026
04:35
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Published on: July 3, 2020
Parametric invariant random matrix model and the emergence of multifractality
J A Méndez-Bermúdez1, Tsampikos Kottos, Doron Cohen
1Max-Planck-Institut für Dynamik und Selbstorganisation, Bunsenstrasse 10, D-37073 Göttingen, Germany.
Summary
We introduce a random matrix model for evolving quantum states in chaotic systems. This model exhibits parametric invariance and a breakdown, leading to multifractality.
Area of Science:
- Quantum mechanics
- Statistical physics
- Chaos theory
Background:
- Eigenstates in quantized chaotic systems exhibit complex parametric evolution.
- Understanding the behavior of these systems is crucial for various fields in physics.
Purpose of the Study:
- To propose a novel random matrix model for describing the parametric evolution of eigenstates.
- To investigate the properties of this model, including parametric invariance and nonperturbative breakdown.
- To explore the emergence of multifractality in these systems.
Main Methods:
- Development of a random matrix model.
- Analysis of parametric invariance.
- Investigation of nonperturbative breakdown phenomena.
- Study of the crossover to multifractality.
Main Results:
- The proposed model demonstrates parametric invariance.
- The model exhibits nonperturbative breakdown, consistent with Wigner's earlier predictions.
- A novel crossover to multifractality is observed within the model.
Conclusions:
- The random matrix model provides a valuable framework for understanding parametric evolution in quantized chaotic systems.
- The model's features, including parametric invariance and breakdown, offer new insights into quantum chaos.
- The emergence of multifractality highlights the complex spectral properties of these systems.
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