2018/09/13 by O. Benichou, Olivier Bénichou, Pierre Illien +7 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Anomalous diffusion #Anomaly (physics) #Condensed matter physics #Diffusion #Geology #Material Dynamics and Properties #Nuclear physics #Particle (ecology) #Physics #Quantum mechanics #Statistical physics #Stochastic processes and statistical mechanics #TRACER #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech #math.PR #physics.bio-ph
paper · pdf · doi:10.1088/1361-648x/aae13a
32 pages, 4 figures, Journal of Physics: Condensed Matter, to appear
arxiv created 2018/09/13 · openalex publication_date 2018/09/13 · arxiv updated 2018/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.