Tag diffusion in driven systems, growing interfaces, and anomalous fluctuations

Abstract

Tagged diffusion in a one-dimensional hard-core lattice gas with biased nearest-neighbor hopping is mapped to a model of a growing interface. Based on the Kardar-Parisi-Zhang theory of interface dynamics, it is suggested that fluctuations, in the separation of the initial position of a tagged particle from the position at time t of a particle with tag shifted by νt at time t, grow at ${\mathit{t}}^{1/2}$ for most ν, and as ${\mathit{t}}^{1/3}$ for a critical ${\nu }_{\mathit{c}}$. This is verified by numerical simulation, and the dependence of ${\nu }_{\mathit{c}}$ on bias and density is found. The ${\mathit{t}}^{1/4}$ growth of fluctuations in the unbiased case is unstable with respect to both bias and ν-${\nu }_{\mathit{c}}$.