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

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Condensed Matter Theory

Background:

• Single-file diffusion is crucial for understanding particle transport in confined systems.
• The one-dimensional symmetric exclusion process (1D-SEP) serves as a fundamental model for such phenomena.
• Investigating open systems with external reservoirs reveals complex dynamics.

Purpose of the Study:

• To model single-file diffusion of hard-core particles using the 1D-SEP.
• To analyze the behavior of an open semi-infinite system coupled to a reservoir.
• To calculate time-dependent correlation functions and particle flux statistics.

Main Methods:

• Exact calculation of the time-dependent two-point density correlation function.
• Determination of the mean and variance of the integrated net particle flux.
• Analysis of a 1D-SEP in an open semi-infinite geometry with a nonequilibrium initial state.

Main Results:

• The boundary region of the relaxing semi-infinite system exhibits behavior analogous to a finite stationary system under a boundary gradient.
• Rigorous proof of this boundary-bulk duality is established using equal-time two-point correlation functions.
• The study provides exact analytical results for a complex nonequilibrium system.

Conclusions:

• The 1D-SEP offers a tractable model for understanding nonequilibrium phenomena in diffusion.
• Findings have implications for the relaxational dynamics of entangled polymers.
• The results are relevant for interpreting single-file diffusion experiments in colloidal systems.