Particle model for the reservoirs in the simple symmetric exclusion process

TL;DR

This paper investigates the long-term behavior of the symmetric exclusion process in a finite channel with large reservoirs, analyzing how different rescaling times affect the system's dynamics.

Contribution

It introduces a particle model for reservoirs in the symmetric exclusion process and studies their impact on the system's long-time behavior under various rescaling regimes.

Findings

Rescaling time influences the process's asymptotic behavior

Large reservoirs significantly affect particle exchange dynamics

Different regimes lead to distinct limiting behaviors

Abstract

In this paper, we will study the long time behavior of the simple symmetric exclusion process in the ``channel'' $\Lambda_N=[1,N]\cap \mathbb{N}$ with reservoirs at the boundaries. These reservoirs are also systems of particles which can be exchanged with the particles in the channel. The size $M$ of each reservoir is much larger than the one of the channel, i.e. $M=N^{1+\alpha}$ for a fixed number $\alpha>0$. Based on the size of the channel and the holding time at each reservoir, we will investigate some types of rescaling time.