2015/05/18 by Tridib Sadhu, Bernard Derrida · 2 citations
Mathematics · Physics and Astronomy · #Anomalous diffusion #Brownian motion #Computer science #Diffusion #Diffusion process #Displacement (psychology) #Distribution (mathematics) #Function (biology) #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Physics #Position (finance) #Quantum mechanics #Realization (probability) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #TRACER #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2015/09/p09008
published as J. Stat. Mech. (2015) P09008 · 21 pages, 1 figure, submitted to a special issue of J Stat Mech
arxiv created 2015/05/18 · openalex publication_date 2015/09/08 · arxiv updated 2016/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Diffusion of impenetrable particles in a crowded one-dimensional channel is referred as the single file diffusion. The particles do not pass each other and the displacement of each individual particle is sub-diffusive. We analyse a simple realization of this single file diffusion problem where one dimensional Brownian point particles interact only by hard-core repulsion. We show that the large deviation function which characterizes the displacement of a tracer at large time can be computed via a mapping to a problem of non-interacting Brownian particles. We confirm recently obtained results of the one time distribution of the displacement and show how to extend them to the multi-time correlations. The probability distribution of the tracer position depends on whether we take annealed or quenched averages. In the quenched case we notice an exact relation between the distribution of the tracer and the distribution of the current. This relation is in fact much more general and would be valid for arbitrary single file diffusion. It allows in particular to get the full statistics of the tracer position for the symmetric simple exclusion process (SSEP) at density 1/2 in the quenched case.