Je. Santos et Gm. Schutz, Exact time-dependent correlation functions for the symmetric exclusion process with open boundary - art. no. 036107, PHYS REV E, 6403(3), 2001, pp. 6107
As a simple model for single-file diffusion of hard core particles we inves
tigate 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 densi
ty correlation function C(k,)l(t)not equivalent to <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 i
n 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 tw
o-point correlation functions. Some implications for the relaxational dynam
ics of entangled polymers and for single-file diffusion in colloidal system
s are discussed.