Coulomb-interacting billiards in circular cavities

We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. 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 more …