Enhancement of Brownian motion for a chain of particles in a periodic potential

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. This is the simplest system which is dynamically rich enough to exhibit an autoparametric excitation of the internal vibrations by the center of mass motion. The consequences of this autoparametric excitation on the particles diffusion will be discussed according to the stiffness of the interaction and to the initial energy of the dimer, the relevant parameters which characterize this dynamics.

Transverse single-file diffusion and enhanced longitudinal diffusion near a subcritical bifurcation

A quasi-one-dimensional system of repelling particles undergoes a configurational phase transition when the transverse confining potential decreases. Below a threshold, it becomes energetically favorable for the system to adopt one of two staggered raw patterns, symmetric with respect to the system axis. This transition is a subcritical pitchfork bifurcation for short range interactions. As a consequence, the homogeneous zigzag pattern is unstable in a finite zigzag amplitude range [h_{C1},h_{C2}]. We exhibit strong qualitative effects of the subcriticality on the thermal motions of the particles. When the zigzag amplitude is close enough to the limits h_{C1} and h_{C2}, a transverse vibrational soft mode occurs which induces a strongly subdiffusive behavior of the transverse fluctuations, similar to single-file diffusion. On the contrary, the longitudinal fluctuations are enhanced, with a diffusion coefficient which is more than doubled. Conversely, a simple measurement of the thermal fluctuations allows a precise determination of the bifurcation thresholds.