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Long time algebraic relaxation in chaotic billiards
Douglas Armstead1, Brian R Hunt, Edward Ott
1University of Maryland, College Park, Maryland 20742, USA. dna2@physics.umd.edu
Physical Review Letters
|January 7, 2003
Summary
The long-time relaxation in periodic billiards exhibits a self-similar form. This behavior is consistent across many billiards but has a notable exception in a specific case.
Area of Science:
- Physics
- Mathematical Physics
- Dynamical Systems
Background:
- Spatially periodic billiards with infinite horizons are complex dynamical systems.
- Understanding their long-time behavior is crucial for statistical mechanics and chaos theory.
Purpose of the Study:
- To investigate the time-asymptotic relaxation process in spatially periodic billiards.
- To identify and characterize the self-similar form of this relaxation.
Main Methods:
- Analysis of the algebraic relaxation process.
- Mathematical modeling of spatially periodic billiards with infinite horizons.
Main Results:
- The long-time relaxation process demonstrates a self-similar time-asymptotic form.
- This form is uniform across a broad class of these billiards.
- A distinct form emerges in a specific, important special case.
Conclusions:
- The self-similar relaxation provides a universal description for many periodic billiard systems.
- The identified special case warrants further investigation due to its unique behavior.