One-particle and few-particle billiards.

Journal article

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.

Authors: Lansel, S; Porter, M; Bunimovich, L

• Publication status: Published
• Journal: Chaos (Woodbury, N.Y.)
• Volume: 16
• Issue: 1
• Pages: 013129
• Publication date: 2006-03-01
• DOI: 10.1063/1.2147740
• EISSN: 1089-7682
• ISSN: 1054-1500
• Language: English