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Geometry-Induced Superdiffusion in Driven Crowded Systems

Olivier Bénichou, Anna Bodrova, Dipanjan Chakraborty, Pierre Illien, Adam Law, Carlos Mejía-Monasterio, Gleb Oshanin, and Raphaël Voituriez
Phys. Rev. Lett. 111, 260601 – Published 26 December 2013
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    Abstract

    Recent molecular dynamics simulations of glass-forming liquids revealed superdiffusive fluctuations associated with the position of a tracer particle (TP) driven by an external force. Such an anomalous response, whose mechanism remains elusive, has been observed up to now only in systems close to their glass transition, suggesting that this could be one of its hallmarks. Here, we show that the presence of superdiffusion is in actual fact much more general, provided that the system is crowded and geometrically confined. We present and solve analytically a minimal model consisting of a driven TP in a dense, crowded medium in which the motion of particles is mediated by the diffusion of packing defects, called vacancies. For such nonglass-forming systems, our analysis predicts a long-lived superdiffusion which ultimately crosses over to giant diffusive behavior. We find that this trait is present in confined geometries, for example long capillaries and stripes, and emerges as a universal response of crowded environments to an external force. These findings are confirmed by numerical simulations of systems as varied as lattice gases, dense liquids, and granular fluids.

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    • Received 30 October 2013

    DOI:https://doi.org/10.1103/PhysRevLett.111.260601

    © 2013 American Physical Society

    Authors & Affiliations

    Olivier Bénichou1,*, Anna Bodrova2, Dipanjan Chakraborty3, Pierre Illien1,*, Adam Law3, Carlos Mejía-Monasterio4, Gleb Oshanin1, and Raphaël Voituriez1,5

    • 1Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France
    • 2Department of Physics, Moscow State University, Moscow 119991, Russia
    • 3Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany, and IV Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
    • 4Laboratory of Physical Properties, Technical University of Madrid, Avenida Complutense s/n, 28040 Madrid, Spain, and Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014 Helsinki, Finland
    • 5Laboratoire Jean Perrin, FRE 3231 CNRS/UPMC, 4 Place Jussieu, 75255 Paris Cedex, France

    • *Corresponding author.

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    Vol. 111, Iss. 26 — 27 December 2013

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    Images

    • Figure 1
      Figure 1
      The model; a discrete lattice in which sites are occupied by identical hard-core medium particles (blue spheres). The red sphere denotes the tracer particle (TP) which, in addition to hard-core interactions, is subject to an external force F=Fe1, and thus has asymmetric hopping probabilities. The arrows of different size depict schematically the hopping probabilities; a larger arrow near the TP indicates that it has a preference for moving in the direction of the applied field. Jumps are possible only when a vacancy (in concentration ρ0) is adjacent to a particle.Reuse & Permissions
    • Figure 2
      Figure 2
      Studied geometries and reduced variance as a function of time in the superdiffusion regime. (a) Sketch of stripe- and capillarylike geometries. (b) Simulations in capillaries [empty symbols, ϕ(t)=3π/2L2/(4a02ρ0t)σx2(t)] and stripes [filled symbols, ϕ(t)=3πL/(8a02ρ0t)σx2(t)] with density ρ0=10−5, and theoretical prediction (solid line, t). (c) Simulations on a 2D lattice with density ρ0=10−5 and ϕ(t)=π2a0[σx2(t)/(ρ0a0t)−(2a0/π)(ln8+γ−1)−2a0π(5−2π)/(2π−4)−coth(f/2)] and theoretical prediction (solid line, lnt). (d) Simulations on a 3D lattice with density ρ0=10−6 and ϕ(t)=[σx2(t)/(ρ0t)−a0coth(f/2)]/(2a02) and theoretical prediction [solid line: A, defined after Eq. (1)].Reuse & Permissions
    • Figure 3
      Figure 3
      Top: rescaled variance as a function of rescaled time ρ02t on stripelike lattices (L=3) for different densities [solid line, g(ρ02t)]; see the Supplemental Material [20]. Bottom: rescaled variance ϕ(t)=σx2(t)/(ρ0t)−(2a02/π)ln(1/ρ02a02) as a function of rescaled time ρ02t on a 2D infinite lattice for different densities [solid line, h(ρ02t)] with h(x)=(2a02/π)ln[a02x/(1+a02x)]+a0coth(f/2)+2a02π(5−2π)/(2π−4)+(2a02/π)(ln8+γ−1).Reuse & Permissions
    • Figure 4
      Figure 4
      Rescaled variance Lσx2(t)/v2 as a function of time obtained from off-lattice simulations for different widths of stripes L and forces f (it can be shown that v∼a0 in the superdiffusion regime). CF: molecular dynamics of colloidal fluids in confined striplike geometries. GF: simulations of dense monodisperse granular fluid in confined striplike geometries; e stands for the restitution parameter. More details on off-lattice simulations are given in the Supplemental Material [20].Reuse & Permissions
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