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Parametric evolution of eigenstates: beyond perturbation theory and semiclassics
J A Méndez-Bermúdez1, Tsampikos Kottos, Doron Cohen
1Max-Planck-Institute for Dynamics and Self-Organnization, 37073 Göttingen, Germany.
Summary
Investigating quantized chaotic systems, this study reveals how eigenstates change with control parameters. A unique "twilight regime" shows both perturbative and semiclassical traits, unlike simpler random-matrix models.
Area of Science:
- Quantum chaos
- Condensed matter physics
- Statistical mechanics
Background:
- Quantized chaotic systems exhibit complex dynamics.
- Understanding transitions between perturbative and non-perturbative regimes is crucial.
- Aharonov-Bohm billiards offer a physical platform for studying quantum chaos.
Purpose of the Study:
- To analyze the evolution of eigenstates in a quantized chaotic system.
- To investigate the crossover from perturbative to non-perturbative regimes.
- To explore the behavior of an Aharonov-Bohm cylindrical billiard under varying magnetic flux.
Main Methods:
- Analysis of eigenstate evolution under parameter variation.
- Examination of local density of states structural changes.
- Study of an Aharonov-Bohm cylindrical billiard model.
Main Results:
- A crossover to a non-perturbative regime is observed with increasing perturbation.
- Structural changes in the local density of states indicate this crossover.
- An intermediate
- twilight regime
- was identified in the Aharonov-Bohm billiard.
- This regime exhibits coexistence of perturbative and semiclassical features.
Conclusions:
- The behavior of quantized chaotic systems differs from random-matrix models.
- The Aharonov-Bohm billiard displays a unique transitional regime.
- Perturbative and semiclassical physics can coexist in specific quantum chaotic systems.