Dissimilar bouncy walkers

Abstract

We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants xi_n, where n labels different bouncy walkers, are drawn from a distribution rho(xi_n). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when rho(xi_n) is heavy-tailed, rho(xi_n)=A xi_n^(-1-\alpha) (0<alpha<1) for large xi_n, we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q,t), follows a Mittag-Leffler relaxation, and the the mean square displacement of a tracer particle (MSD) grows as t^delta with time t, where delta=alpha/(1+\alpha). If instead rho is light-tailedsuch that the mean friction constant exist, S(Q,t) decays exponentially and the MSD scales as t^(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model.