Transverse single-file diffusion near the zigzag transition

Jean-Baptiste Delfau (1) , Christophe Coste (1) , Michel Saint-Jean (1)

1 MSC (UMR_7057) - Matière et Systèmes Complexes

We study with numerical simulations the transverse fluctuations in quasi-one-dimensional systems of particles in a thermal bath, near the zigzag transition. We show that close to the zigzag threshold, the transverse fluctuations exhibit an anormal diffusion, characterized by a mean square displacement that increases as the square root of time. In contrast with the longitudinal fluctuations, this behavior of the transverse fluctuations cannot be explained by the single-file ordering. We provide an analytical modelization, and in the thermodynamic limit we demonstrate the existence of this subdiffusive regime near the zigzag transition, showing that it results from overdamped collective modes of the system. These calculations are extended to finite systems, in excellent agreement with the simulations data. We also exhibit some effects of the thermal fluctuations on the zigzag transition, and analyze them in the light of stochastic bifurcation theory.

Domains: Physics [physics]; Condensed Matter [cond-mat]

Jean-Baptiste Delfau, Christophe Coste, Michel Saint-Jean. Transverse single-file diffusion near the zigzag transition. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2013, 87, pp.32163 - 32163. ⟨10.1103/PhysRevE.87.032163⟩. ⟨hal-01404826⟩