Correlation effects of two interacting particles in a circular billiard

The maximal Lyapunov exponent is determined numerically for two classical unequal-mass interacting particles inside a circular billiard and subjected to a static magnetic field. A Yukawa potential is used for the interaction between the particles. Transitions from short to long interaction ranges and from equal to infinite mass ratio between particles are discussed. Correlations effects between particles strongly determine the dynamics inside the billiard. A qualitative change in the Lyapunov exponent dependence on the interaction range between particles is observed by the transition from weak to strong couplings. Poincaré surfaces of section are also used to describe the dynamics in the limit of infinite mass ratio.