Dissimilar bouncy walkers

TL;DR

This paper analyzes the dynamics of dissimilar hardcore interacting random walkers in one dimension, revealing new universality classes based on the distribution of their friction constants and providing approximate solutions supported by simulations.

Contribution

It introduces an approximate analytic solution for dissimilar bouncy walkers using harmonization and effective medium techniques, identifying new universality classes based on friction constant distributions.

Findings

Heavy-tailed friction distribution leads to Mittag-Leffler relaxation and MSD ~ t^delta.

Light-tailed friction distribution results in exponential decay and MSD ~ t^(1/2).

Results are supported by simulations and simplified models.

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.