Motions of a dimer on a periodic potential

A dimer on a periodic potential is a simple system that exhibits a surprisingly rich dynamics. This system is conservative, but it is nonlinear and nonintegrable. In a previous work, we evidenced the autoparametric excitation of the relative motion by the center of mass in two limiting cases (very small or very large initial energy, compared to the external potential depth). We extend these results for arbitrary initial energy. The relevant control parameters are the dimer initial energy and the stiffness of the link between the two particles. In this parameter plane, we build a behavior map which classifies the available dynamical regimes of the dimer. The parameters plane can be separated into domains in which the dimer particles are either trapped in adjacent potential wells, slide along the potential, or exhibit more complex motions in which the particles jumps to farthest well or in which the center-of-mass motion is neither monotonous nor periodic. We discuss the thresholds between these domains.