Dynamics of two interacting particles in classical billiards

Details Dynamics of two interacting particles in classical billiards Dynamics of two interacting particles in classical billiards

1997-03-10

arxiv.org/abs/cond-mat/9703098v1

Physics

Condensed Matter

REVTEX manuscript, 4 figures (1 ps + 3 gif, Postscript versions available upon request). Also available at http://www.phy.oh

Scientific paper

10.1103/PhysRevE.55.R6319

The problem of two interacting particles moving in a d-dimensional billiard is considered here. A suitable coordinate transformation leads to the problem of a particle in an unconventional hyperbilliard. A dynamical map can be readily constructed for this general system, which greatly simplifies calculations. As a particular example, we consider two identical particles interacting through a screened Coulomb potential in a one-dimensional billiard. We find that the screening plays an important role in the dynamical behavior of the system and only in the limit of vanishing screening length can the particles be considered as bouncing balls. For more general screening and energy values, the system presents strong non-integrability with resonant islands of stability.

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