Anomalous field-induced growth of fluctuations in dynamics of a biased intruder moving in a quiescent medium

Abstract

We present exact results on the dynamics of a biased, by an external force $\mathbf{F}$, 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 $P({\mathbf{R}}_n)$ of the BI displacement ${\mathbf{R}}_n$ at time {\it n}. We show that despite the fact that the BI drives the gas to a non-equilibrium steady-state, $P({\mathbf{R}}_n)$ converges to a Gaussian distribution as $n\to \infty$. We find that the variance ${\sigma }_x^2$ of $P({\mathbf{R}}_n)$ along $\mathbf{F}$ exhibits a weakly superdiffusive growth ${\sigma }_x^2\sim {\nu }_{1}n\ln (n)$, and a usual diffusive growth, ${\sigma }_y^2\sim {\nu }_{2}n$, in the perpendicular direction. We determine ${\nu }_1$ and ${\nu }_2$ exactly for arbitrary bias, in the lowest order in the density of vacancies, and show that ${\nu }_1\sim |\mathbf{F}{|}^2$ for small bias, which signifies that superdiffusive behaviour emerges beyond the linear-response approximation. Monte Carlo simulations confirm our analytical results, and reveal a striking field-induced superdiffusive behavior ${\sigma }_x^2\sim n^{3/2}$ for infinitely long 2D stripes and 3D capillaries.

5 pages, 3 figures, RevTeX style

References in corpus (3)

• Anomalous diffusion of driven particles in supercooled liquids
• Colloids dragged through a polymer solution: experiment, theory and simulation
• Colloid-colloid and colloid-wall interactions in driven suspensions

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