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

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 {ν}t at time t, grow at t1/2 for most {ν}, and as t1/3 for a critical νc. This is verified by numerical simulation, and the dependence of νc on bias and density is found. The t1/4 growth of fluctuations in the unbiased case is unstable with respect to both bias and {ν}-νc.