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Dynamical properties of the soft-wall elliptical billiard
Tiago Kroetz1,2, Hércules A Oliveira3, Jefferson S E Portela1
1Departamento Acadêmico de Física, Universidade Tecnológica Federal do Paraná-UTFPR Campus Pato Branco, Pato Branco 85503-390, PR, Brazil.
Physical Review. E
|September 15, 2016
Summary
Investigating soft-walled elliptical billiards reveals that wall softness introduces chaos, unlike their hard-walled counterparts. The degree of chaos is complexly related to wall hardness and billiard shape.
Area of Science:
- Physics
- Dynamical Systems
- Mathematical Physics
Background:
- Physical systems like optical traps and microwave cavities are often modeled as billiards.
- Realistic models require considering soft walls, deviating from idealized hard-wall models.
Purpose of the Study:
- To investigate the influence of wall softness on billiard dynamics.
- To analyze the transition from regular to chaotic behavior in soft-walled elliptical billiards.
Main Methods:
- Numerical study of a smooth two-dimensional potential well.
- Analysis of systems with varying eccentricity and wall hardness parameters.
Main Results:
- The hard-wall elliptical billiard limit is integrable and regular.
- Soft-walled elliptical billiards exhibit chaotic dynamics.
- Chaotic fraction depends non-monotonically on wall hardness.
- The impact of hardness is strongly dependent on billiard eccentricity.
Conclusions:
- Wall softness is a crucial factor in billiard dynamics, inducing chaos.
- Findings suggest generalization to other quasi-integrable systems, like the limaçon billiard, which can show enhanced chaos.
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