Exact time-dependent correlation functions for the symmetric exclusion process with open boundary.

As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant density rho(*) and which initially is in a nonequilibrium state with bulk density rho(0). We calculate the exact time-dependent two-point density correlation function C(k,l)(t) identical with<n(k)(t)n(l)(t)>-<n(k)(t)><n(l)(t)> and the mean and variance of the integrated average net flux of particles N(t)-N(0) that have entered (or left) the system up to time t. We find that the boundary region of the semi-infinite relaxing system is in a state similar to the bulk state of a finite stationary system driven by a boundary gradient. The symmetric exclusion model provides a rare example where such behavior can be proved rigorously on the level of equal-time two-point correlation functions. Some implications for the relaxational dynamics of entangled polymers and for single-file diffusion in colloidal systems are discussed.