Dissimilar bouncy walkers

Summary, in English

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.

• Author: Michael A Lomholt; Ludvig Lizana; Tobias Ambjörnsson
• Department/s: Computational Biology and Biological Physics - Undergoing reorganization
• Publishing year: 2011
• Language: English
• Publication/Series: Journal of Chemical Physics
• Volume: 134
• Issue: 4
• Links: http://dx.doi.org/10.1063/1.3526941
• Document type: Journal article
• Publisher: American Institute of Physics (AIP)
• Topic: Biophysics; Other Physics Topics
• Status: Published
• ISBN/ISSN/Other: ISSN: 0021-9606