Tracer and Current Fluctuations in Driven Diffusive Systems

Interacting particles diffusing in single file is a fundamental model of transport in narrow channels where particles cannot bypass each other. An important result has been obtained by Kollmann [Phys. Rev. Lett. 90, 180602 (2003)PRLTAO0031-900710.1103/PhysRevLett.90.180602] for the mean square displacement of a tracer for any single-file model. It applies to any diffusive system, in particular the notable classes of colloidal systems and diffusive stochastic lattice gases. Since then, no analog result has been obtained in the important case where the particles are driven by an external field. Here, we fill this gap and determine the fluctuations and the skewness of the tracer's position for any driven diffusive system. In addition, we also consider a variety of important observables such as the integrated current, the response of the system to the perturbation induced by the displacement of the tracer, and the correlations between several tracers. Furthermore, we also unveil fundamental relations underlying the out-of-equilibrium dynamics of driven diffusive systems. This work constitutes a step toward the determination of the full distribution of all these observables in driven one-dimensional systems of interacting particles.