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Periodic chaotic billiards: quantum-classical correspondence in energy space
G A Luna-Acosta1, J A Méndez-Bermúdez, F M Izrailev
1Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.
Summary
We explored quantum-classical correspondence in rippled billiards. Classical dynamics, especially periodic orbits, explain quantum properties like eigenstates and local density of states (LDOS).
Area of Science:
- Quantum mechanics
- Classical mechanics
- Statistical physics
Background:
- Investigating quantum-classical correspondence in complex systems is crucial for understanding their behavior.
- Rippled billiards offer a unique platform to study quantum phenomena due to their intricate boundary effects.
Purpose of the Study:
- To examine the quantum-classical correspondence of eigenstates and local density of states (LDOS) in a periodic 2D rippled billiard.
- To understand how classical dynamics, particularly periodic orbits, influence quantum properties.
Main Methods:
- Incorporating boundary effects via canonical transformation to create an effective potential.
- Equating 2D rippled billiard motion to a 1D two-interacting-particle system.
- Analyzing the correspondence between quantum quantities and their classical counterparts.
Main Results:
- A good quantum-classical correspondence was found for structure of eigenstates (SES) and LDOS in strongly chaotic regimes.
- Classical dynamics and periodic orbits effectively explain key features of SES and LDOS.
- Statistical properties of eigenstates and LDOS deviate from random matrix theory predictions.
Conclusions:
- The study highlights the significant role of classical dynamics in understanding quantum properties of rippled billiards.
- Quantum effects contribute to the non-ergodic nature of eigenstates and LDOS, a common characteristic in such systems.