Dissimilar bouncy walkers
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Abstract
We consider the dynamics of a onedimensional 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 singlefile problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when ϱ(ξ(n)) is heavytailed, ϱ(ξ(n))≃ξ(n) (1α) (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 MittagLeffler 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 lighttailed 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.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY

Original language  English 

Article number  045101 
Journal  Journal of Chemical Physics 
Volume  134 
Issue number  4 
Publication status  Published  2011 
Publication category  Research 
Peerreviewed  Yes 