title: 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 ξ(n), where n labels different bouncy walkers, are drawn from a distribution ϱ(ξ(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 ϱ(ξ(n)) is heavy-tailed, ϱ(ξ(n))≃ξ(n) (-1-α) (0<α<1) for large ξ(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 mean square displacement (MSD) of a tracer particle grows as t(δ) with time t, where δ = α∕(1 + α). If instead ϱ is light-tailed such 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.
authors.affiliation: MEMPHYS-Center for Biomembrane Physics, Department of Physics and Chemistry, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Lomholt
authors.forename: Ludvig
authors.initials: L
authors.lastname: Lizana
authors.forename: Tobias
authors.initials: T
authors.lastname: Ambjörnsson
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D017276:Friction; D008956:Models, Chemical; D015233:Models, Statistical; D009038:Motion; D011336:Probability; D013997:Time Factors