Diffusion enhancement and autoparametric resonance.

The possibility of an autoparametric resonance in an isolated many-particle system induces a specific behavior of the particles in the presence of thermal noise. In particular, the variance associated with a resonant mode, and consequently that of the associated particles, is strongly increased compared to what it would have in the absence of parametric resonance. In this paper we consider a dimer submitted to a periodic potential for which there are only two modes, the center of mass motion and the internal vibration mode.

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).

Parametric resonance in a conservative system of coupled nonlinear oscillators.

We study a dimer in a periodic potential well, which is a conservative but nonintegrable system. This seemingly simple system exhibits a surprisingly rich dynamics. Using a systematic asymptotic analysis, we demonstrate that the translation mode of the dimer (center of mass motion) may induce a parametric resonance of the oscillatory mode.