Nonequilibrium Fluctuations and Enhanced Diffusion of a Driven Particle in a Dense Environment

Pierre Illien, Olivier Bénichou, Gleb Oshanin, Alessandro Sarracino, and Raphaël Voituriez

Phys. Rev. Lett. 120, 200606 – Published 16 May 2018

Abstract

We study the diffusion of a tracer particle driven out of equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced by both the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.

Received 18 July 2017
Revised 2 January 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.200606

Physics Subject Headings (PhySH)

Diffusion Nonequilibrium statistical mechanics Random walks

Statistical Physics & Thermodynamics

Authors & Affiliations

Pierre Illien^1,2,*, Olivier Bénichou³, Gleb Oshanin³, Alessandro Sarracino^4,5, and Raphaël Voituriez^3,6

¹Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
²Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
³Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France
⁴Istituto dei Sistemi Complessi-CNR, P.le Aldo Moro 2, 00185 Rome, Italy
⁵Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
⁶Laboratoire Jean Perrin, CNRS UMR 8237, Université Pierre-et-Marie-Curie, 4 Place Jussieu, 75005 Paris, France