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Quantum chaos and physical distance between quantum states.
Zhenduo Wang1, Yijie Wang1, Biao Wu1,2,3
1International Center for Quantum Materials, School of Physics, Peking University, 100871 Beijing, China.
Physical Review. E
|May 19, 2021
Summary
Researchers introduce a novel physical distance for quantum states, revealing genuine quantum chaos. This new measure allows for the definition of quantum Lyapunov exponents and chaos measures, distinguishing regular from chaotic quantum dynamics.
Area of Science:
- Quantum Mechanics
- Chaos Theory
- Quantum Dynamics
Background:
- Existing distance measures for quantum states, like Fubini-Study, do not fully capture the nuances of quantum dynamics.
- The emergence of chaos in quantum systems remains a complex and actively researched area.
Purpose of the Study:
- To introduce a new physical distance metric for quantum states.
- To demonstrate the existence of genuine chaos in quantum dynamics using this new metric.
- To develop tools for quantifying and visualizing quantum chaos.
Main Methods:
- Introduction of a novel physical distance between quantum states.
- Definition of quantum Lyapunov exponent and quantum chaos measure based on physical distance.
- Application of the methods to diverse quantum systems: kicked rotor, Bose-Hubbard model, and XXZ model.
Main Results:
- The physical distance between orthogonal quantum states can be arbitrarily small, unlike other metrics.
- Quantum states initially close in physical distance can diverge significantly during evolution, indicating chaos.
- A quantum analog of the Poincaré section was developed, differentiating regular and chaotic dynamics.
Conclusions:
- Genuine quantum chaos is demonstrated through a new physical distance measure.
- The developed measures provide a robust framework for analyzing quantum chaos.
- The findings offer new insights into the behavior of complex quantum systems.
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