Single-file diffusion on self-similar substrata

G. P. SUÁREZ; H. O. MÁRTIN; J. L. IGUAIN

Workshop; XIII Latin American Workshop on Nonlinear Phenomena; 2013

The diffusion of particles, interacting through a hard-core potential, in an one-dimensional infinite lattice is known as single file diffusion. Double occupancy and jumps over other particles are not allowed. It is well known that the mean square displacement of a tagged particle behaves as D^2 x ~ t^2 and presents two regimes: normal diffusion (nu = 1/2) for short times, and a sub-diffusive regime (nu = 1/4) for long times. Modifying the substrate on which the particles move, it is possible to change its time behavior. In particular, if we place barriers on a self-similar arrangement the time dependence of the mean square displacement is now modulated by logarithmic-periodic oscillations. In this work we use simple arguments to explain these oscillations and how the diffusion of the center of mass is affected. We also found a expression for the new exponents in both regimes and investigated the effect of changing the concentration of particles. Monte Carlo simulations were used to confirm theoretical results.