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Phase-space correlations of chaotic eigenstates
1Max-Planck-Institut für Dynamik und Selbstorganisation, Universität Göttingen, Germany. holger@chaos.gwdg.de
Physical Review Letters
|May 21, 2005
Summary
Chaotic eigenstates show strong correlations along classical trajectories, persisting in the semiclassical limit. This finding, explained by Gaussian wave packet dynamics, offers new insights into quantum chaos.
Area of Science:
- Quantum mechanics
- Chaos theory
- Statistical physics
Background:
- Understanding quantum chaos is crucial for various fields.
- Eigenstate properties in the semiclassical limit are not fully understood.
- Husimi representations offer a phase-space view of quantum states.
Purpose of the Study:
- To investigate correlations in Husimi representations of chaotic eigenstates.
- To explore the behavior of these correlations in the semiclassical limit.
- To develop a theoretical framework explaining these observed correlations.
Main Methods:
- Analysis of Husimi representations of chaotic eigenstates.
- Investigation of correlations across different system sizes.
- Development of a quantitative theory using Gaussian wave packet dynamics.
- Application of random-matrix arguments.
- Discussion of symmetry roles, including time-reversal invariance.
Main Results:
- Husimi representations of chaotic eigenstates exhibit strong correlations along classical trajectories.
- These correlations are system-spanning.
- Correlations persist in the semiclassical limit, unlike configuration-space eigenfunction correlations.
- A quantitative theory successfully describes these phenomena.
Conclusions:
- Chaotic eigenstates possess unique correlation properties in phase space.
- The developed theory provides a robust explanation for these correlations.
- Symmetries play a significant role in shaping these quantum chaotic behaviors.