Exact correlations in a single-file system with a driven tracer

¹ International center for theoretical sciences, TIFR - Bangalore-560012, India
² Department of Physics of Complex Systems, Weizmann Institute of Science - Rehovot 76100, Israel

Received: 10 August 2016
Accepted: 15 September 2016

Abstract

We study the effect of a single driven tracer particle in a bath of other particles performing the random average process on an infinite line using a stochastic hydrodynamics approach. We consider arbitrary fixed as well as random initial conditions and compute the two-point correlations. For quenched uniform and annealed steady-state initial conditions we show that in the large time T limit the fluctuations and the correlations of the positions of the particles grow subdiffusively as and have well-defined scaling forms under proper rescaling of the labels. We compute the corresponding scaling functions exactly for these specific initial configurations and verify them numerically. We also consider a non-translationally invariant initial condition with linearly increasing gaps where we show that the fluctuations and correlations grow superdiffusively as at large times.