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

Fuente: arXiv
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Main Authors: Berlioz, Théotim, Venturelli, Davide, Grabsch, Aurélien, Bénichou, Olivier
Format: Preprint
Published: 2024
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author Berlioz, Théotim
Venturelli, Davide
Grabsch, Aurélien
Bénichou, Olivier
author_facet Berlioz, Théotim
Venturelli, Davide
Grabsch, Aurélien
Bénichou, Olivier
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_14317
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
Berlioz, Théotim
Venturelli, Davide
Grabsch, Aurélien
Bénichou, Olivier
Statistical Mechanics
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.
title Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
topic Statistical Mechanics
url https://arxiv.org/abs/2407.14317