Dissimilar bouncy walkers

TY - JOUR

T1 - Dissimilar bouncy walkers

AU - Lomholt, Michael A.

AU - Lizana, George Ludvig

PY - 2011/1/28

Y1 - 2011/1/28

N2 - We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants n, where n labels different bouncy walkers, are drawn from a distribution ( 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 ( n) is heavy-tailed, ( n)≃ n -1- (01) for large 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 with time t, where (1 ). If instead 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.

AB - We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants n, where n labels different bouncy walkers, are drawn from a distribution ( 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 ( n) is heavy-tailed, ( n)≃ n -1- (01) for large 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 with time t, where (1 ). If instead 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.

U2 - 10.1063/1.3526941

DO - 10.1063/1.3526941

M3 - Journal article

C2 - 21280802

SN - 0021-9606

VL - 134

SP - 045101

JO - The Journal of Chemical Physics

JF - The Journal of Chemical Physics

IS - 8

ER -