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Published on: February 22, 2018
Anomalous shell effect in the transition from a circular to a triangular billiard
Ken-Ichiro Arita1, Matthias Brack
1Department of Physics, Nagoya Institute of Technology, 466-8555 Nagoya, Japan.
Summary
We studied chaotic dynamics in a billiard system transitioning from circular to triangular shapes. A significant shell effect was observed, linked to a specific periodic orbit bifurcation, and accurately modeled using semiclassical methods.
Area of Science:
- Physics
- Quantum Mechanics
- Dynamical Systems
Background:
- Billiard systems are fundamental models for studying classical and quantum chaos.
- Understanding shape transitions in dynamical systems is crucial for various physics fields.
Purpose of the Study:
- To investigate the emergence of shell effects in a two-dimensional nonintegrable billiard system undergoing shape transition.
- To analyze the role of periodic orbits and bifurcations in semiclassical dynamics.
Main Methods:
- Application of periodic orbit theory and semiclassical analysis.
- Utilizing Gutzwiller's semiclassical trace formula with global uniform approximation.
- Studying a system smoothly deformed from circular to equilateral triangular boundaries.
Main Results:
- Observed a pronounced shell effect during the shape transition, despite increasing classical chaos.
- Identified a codimension-2 bifurcation of the triangular periodic orbit as the source of the shell effect.
- Demonstrated that the semiclassical trace formula accurately describes the quantum mechanical level density.
Conclusions:
- The shell effect in this system is a robust phenomenon driven by specific orbital dynamics.
- Semiclassical theory provides an accurate framework for understanding quantum properties of chaotic systems.
- Discrete symmetries play a role in enhancing the observed shell effect.
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