One-Particle and Few-Particle Billiards

Details One-Particle and Few-Particle Billiards One-Particle and Few-Particle Billiards

2005-08-30

arxiv.org/abs/nlin/0508037v2

Nonlinear Sciences

Chaotic Dynamics

12 pages, 9 figures (30 total parts; many of them in color, higher quality figures available in version at http://www.its.ca

Scientific paper

10.1063/1.2147740

We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case, we investigate the formation and destruction of resonance islands in (generalized) mushroom billiards, which are a recently discovered class of Hamiltonian systems with mixed regular-chaotic dynamics. In the few-particle case, we compare the dynamics in container geometries whose counterpart one-particle billiards are integrable, chaotic, and mixed. One of our findings is that two-, three-, and four-particle billiards confined to containers with integrable one-particle counterparts inherit some integrals of motion and exhibit a regular partition of phase space into ergodic components of positive measure. Therefore, the shape of a container matters not only for noninteracting particles but also for interacting particles.

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