Non-equilibrium and stationary fluctuations for the SSEP with slow boundary

TL;DR

This paper studies the non-equilibrium and stationary fluctuations of the symmetric simple exclusion process with slow boundary reservoirs, revealing how boundary conditions affect fluctuation behavior and deriving stationary measures.

Contribution

It introduces a detailed analysis of boundary effects on fluctuations in SSEP with slow reservoirs and derives stationary measures using the matrix ansatz method.

Findings

Different boundary conditions depending on the parameter  boundary parameters.

Precise bounds on two-point space-time correlation functions are established.

The stationary measure is characterized using the matrix ansatz method.

Abstract

We derive the non-equilibrium fluctuations of one-dimensional symmetric simple exclusion processes in contact with slowed stochastic reservoirs which are regulated by a factor $n^{-\theta}$. Depending on the range of $\theta$ we obtain processes with various boundary conditions. Moreover, as a consequence of the previous result we deduce the non-equilibrium stationary fluctuations by using the matrix ansatz method which gives us information on the stationary measure for the model. The main ingredient to prove these results is the derivation of precise bounds on the two-point space-time correlation function, which are a consequence of precise bounds on the transition probability of some underlying random walks.