J. Solanpaa, J. Nokelainen, P. J. J. Luukko, E. Rasanen
We apply a molecular dynamics scheme to analyze chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strong-interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits, albeit the dynamics is generally chaotic. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a quantitative view on the degree of chaoticity, we compute the escape rates that, apart from very weak interactions as well as the strong-interaction limit, suggest generally chaotic behavior that is independent of the interaction strength.
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http://arxiv.org/abs/1210.2811
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