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Nonperiodic echoes from mushroom billiard hats
B Dietz1, T Friedrich, M Miski-Oglu
1Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
Investigating mushroom billiards reveals distinct integrable islands within chaotic seas. Chaotic orbits show limited delay times scattering from mushroom hats, suggesting potential for mesoscopic devices.
Area of Science:
- Mathematical Physics
- Dynamical Systems
- Mesoscopic Physics
Background:
- Mushroom billiards exhibit unique integrable islands within chaotic seas, lacking fractal boundaries.
- These islands represent orbits confined to the 'hats' of the mushroom shape.
- Chaotic orbits interact with these integrable islands, posing questions about their dynamics.
Purpose of the Study:
- To investigate the duration chaotic orbits remain within the 'hat' of mushroom billiards.
- To determine the possible delay times for scattering from the mushroom hat into an opening.
- To explore the implications of these delay times for mesoscopic devices.
Main Methods:
- Analysis of chaotic orbits within the mushroom billiard model.
- Calculation of scattering delay times for fixed angular momentum.
- Identification of distinct delay time values.
Main Results:
- For a fixed angular momentum, a maximum of three distinct delay times were identified.
- These delay times exhibit striking nonperiodic structures.
- The findings suggest a unique dynamical behavior within the mushroom billiard system.
Conclusions:
- The limited number of delay times and their nonperiodic structures are significant findings.
- These properties may be crucial for the development of novel mesoscopic devices.
- The phenomena are theoretically accessible and potentially verifiable through microwave experiments.
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