Diffusion and Subdiffusion of Interacting Particles on Comblike Structures

O. Bénichou, P. Illien, G. Oshanin, A. Sarracino, and R. Voituriez
Phys. Rev. Lett. 115, 220601 – Published 25 November 2015
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Abstract

We study the dynamics of a tracer particle (TP) on a comb lattice populated by randomly moving hard-core particles in the dense limit. We first consider the case where the TP is constrained to move on the backbone of the comb only. In the limit of high density of the particles, we present exact analytical results for the cumulants of the TP position, showing a subdiffusive behavior t3/4. At longer times, a second regime is observed where standard diffusion is recovered, with a surprising nonanalytical dependence of the diffusion coefficient on the particle density. When the TP is allowed to visit the teeth of the comb, based on a mean-field-like continuous time random walk description, we unveil a rich and complex scenario with several successive subdiffusive regimes, resulting from the coupling between the geometrical constraints of the comb lattice and particle interactions. In this case, remarkably, the presence of hard-core interactions asymptotically speeds up the TP motion along the backbone of the structure.

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  • Received 2 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.220601

© 2015 American Physical Society

Authors & Affiliations

O. Bénichou, P. Illien, G. Oshanin, A. Sarracino, and R. Voituriez

  • Sorbonne Universités, UPMC Université Paris 06, UMR 7600, LPTMC, F-75005 Paris, France and CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, F-75005 Paris, France

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Issue

Vol. 115, Iss. 22 — 27 November 2015

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