2012/11/04 by Olivier Bénichou, Carlos Mejía-Monasterio, Gleb Oshanin
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Distribution (mathematics) #Gaussian #Lattice (music) #Material Dynamics and Properties #Mathematical analysis #Mathematical physics #Mathematics #Monte Carlo method #Order (exchange) #Physics #Quantum mechanics #Sigma #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.87.020103
5 pages, 3 figures, RevTeX style
arxiv created 2012/11/04 · openalex publication_date 2013/02/13 · arxiv updated 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present exact results on the dynamics of a biased, by an external force F, intruder (BI) in a two-dimensional lattice gas of unbiased, randomly moving hard-core particles. Going beyond the usual analysis of the force-velocity relation, we study the probability distribution P(Rn) of the BI displacement Rn at time n. We show that despite the fact that the BI drives the gas to a nonequilibrium steady state, P(Rn) converges to a Gaussian distribution as n\ensuremath→\ensuremath∞. We find that the variance \ensuremathσx2 of P(Rn) along F exhibits a weakly superdiffusive growth \ensuremathσx2\ensuremath∼\ensuremathν1\phantom\rule0.16em0exn\phantom\rule0.16em0exln(n), and a usual diffusive growth, \ensuremathσy2\ensuremath∼\ensuremathν2\phantom\rule0.16em0exn, in the perpendicular direction. We determine \ensuremathν1 and \ensuremathν2 exactly for arbitrary bias, in the lowest order in the density of vacancies, and show that \ensuremathν1\ensuremath∼|F|2 for small bias, which signifies that superdiffusive behavior emerges beyond the linear-response approximation. We also present analytical arguments predicting a striking field-induced superdiffusive behavior \ensuremathσx2\ensuremath∼n3/2 for two-dimensional stripes and three-dimensional capillaries, which is confirmed by Monte Carlo simulations.