Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry

TL;DR

This paper investigates current fluctuations in the symmetric exclusion process across higher-dimensional and complex lattice geometries, revealing how system dimension and structure influence fluctuation behavior through explicit correlation calculations.

Contribution

It extends the analysis of current fluctuations in SEP beyond 1D by exploring higher-dimensional and comb lattice geometries, providing explicit correlation computations.

Findings

Current fluctuations depend on lattice geometry and dimension.

In higher dimensions, fluctuations exhibit different growth behaviors.

Explicit current-density correlations are derived for various geometries.

Abstract

The symmetric simple exclusion process (SEP) is a paradigmatic model of transport, both in and out-of-equilibrium. In this model, the study of currents and their fluctuations has attracted a lot of attention. In finite systems of arbitrary dimension, both the integrated current through a bond (or a fixed surface), and its fluctuations, grow linearly with time. Conversely, for infinite systems, the integrated current displays different behaviours with time, depending on the geometry of the lattice. For instance, in 1D the integrated current fluctuations are known to grow sublinearly with time, as $\sqrt{t}$. Here we study the fluctuations of the integrated current through a given lattice bond beyond the 1D case by considering a SEP on higher-dimensional lattices, and on a comb lattice which describes an intermediate situation between 1D and 2D. We show that the different behaviours of the current originate from qualitatively and quantitatively different current-density correlations in the systems, which we compute explicitly.