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Hidden quantum-classical correspondence in chaotic billiards revealed by mutual information
Kyu-Won Park1, Soojoon Lee1,2, Kabgyun Jeong2,3
1Kyung Hee University, Department of Mathematics and Research Institute for Basic Sciences, Seoul 02447, Korea.
Physical Review. E
|September 16, 2025
Summary
Quantum chaos in billiards surprisingly enhances correlations between position and momentum, challenging the idea that chaos only leads to delocalization. This finding reveals new insights into quantum-classical correspondence.
Area of Science:
- Quantum mechanics
- Quantum chaos
- Information theory
Background:
- Avoided level crossings in quantum systems are linked to quantum chaos.
- These crossings are often interpreted as signs of eigenstate hybridization and spatial delocalization.
- Spatial delocalization is typically associated with ergodic spreading in quantum systems.
Purpose of the Study:
- To investigate the relationship between quantum chaos and correlations in quantum systems.
- To challenge the conventional interpretation of avoided level crossings and spatial delocalization.
- To explore the role of mutual information in understanding quantum-classical correspondence.
Main Methods:
- Analysis of quantum chaos in quantum billiards.
- Utilizing information-theoretic decomposition of eigenstate entropy.
- Examining mutual information between conjugate phase space variables (position and momentum).
Main Results:
- Increasing quantum chaos enhances mutual information between conjugate phase space variables.
- Spatial delocalization can coexist with increased mutual information between position and momentum.
- These correlations align with classical invariant structures and persist beyond the semiclassical regime.
Conclusions:
- Quantum chaos can lead to non-trivial correlations, not just delocalization.
- Mutual information provides a robust measure of quantum-classical correspondence.
- The findings challenge traditional interpretations and offer new perspectives on quantum chaos.
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