An interacting spin flip model for one-dimensional proton conduction

TL;DR

This paper models one-dimensional proton conduction using a three-state asymmetric exclusion process, analyzing steady-state currents and phase regimes through mean field and Monte Carlo methods.

Contribution

It introduces a three-state ASEP model for proton conduction, providing analysis and comparison with simulations, and discusses potential refinements.

Findings

Mean field results match simulations in certain regimes

Identified regimes analogous to low and maximal current phases

Model can be extended to include more complex forces and defects

Abstract

A discrete asymmetric exclusion process (ASEP) is developed to model proton conduction along one-dimensional water wires. Each lattice site represents a water molecule that can be in only one of three states; protonated, left-pointing, and right-pointing. Only a right(left)-pointing water can accept a proton from its left(right). Results of asymptotic mean field analysis and Monte-Carlo simulations for the three-species, open boundary exclusion model are presented and compared. The mean field results for the steady-state proton current suggest a number of regimes analogous to the low and maximal current phases found in the single species ASEP [B. Derrida, Physics Reports, {\bf 301}, 65-83, (1998)]. We find that the mean field results are accurate (compared with lattice Monte-Carlo simulations) only in the certain regimes. Refinements and extensions including more elaborate forces and pore defects are also discussed.