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

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, randomlymoving hard-core particles. Going beyond the usual analysis of the force-velocity relation, we study the probability distribution P(R-n) of the BI displacement R-n at time n. We show that despite the fact that the BI drives the gas to a nonequilibrium steady state, P(R-n) converges to a Gaussian distribution as n -> 8. We find that the variance sigma(2)(x) of P(R-n) along F exhibits a weakly superdiffusive growth sigma(2)(x) similar to nu(1) n ln(n), and a usual diffusive growth, sigma(2)(y) similar to 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) similar to |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 sigma(2)(x) similar to n(3/2) for two-dimensional stripes and three-dimensional capillaries, which is confirmed by Monte Carlo simulations. DOI: 10.1103/PhysRevE.87.020103