Dissimilar bouncy walkers

الأصل · EN

We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants xiₙ, where n labels different bouncy walkers, are drawn from a distribution rho(xiₙ). 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(xiₙ) is heavy-tailed, rho(xiₙ)=A xiₙ(-1-α) (0<alpha<1) for large xiₙ, 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 tᵈelta with time t, where delta=alpha/(1+α). 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.