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

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

2001-04-09

arxiv.org/abs/cond-mat/0104147v2

Phys. Rev. E 64, 036107 (2001)

Physics

Condensed Matter

Statistical Mechanics

11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference 17 added

Scientific paper

10.1103/PhysRevE.64.036107

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 $\rho^\ast$ and which initially is in an non-equilibrium state with bulk density $\rho_0$. We calculate the exact time-dependent two-point density correlation function $C_{k,l}(t)\equiv - $ 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.

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