Single-file diffusion on self-similar substrata

SUÁREZ, GONZALO PABLO; MÁRTIN, HÉCTOR; IGUAIN, JOSE LUIS

Carlos Paz, Córdoba

Workshop; XIII Latin American Workshop on Nonlinear Phenomena (XIII LAWNP); 2013

The diusion of particles, interacting through a hard-core potential, in an unidimensional 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 ∆2 x ∼ t2ν and presents two regimes: normal diusion (ν= 1/2) for short times, and a sub-diusive regime (ν= 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 an expression for the new exponents ν in both regimes and investigated the effect of changing the concentration of particles. Monte Carlo simulations where used to conffirm theoretical results.