Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory

TL;DR

This paper introduces an exactly solvable multi-species symmetric simple exclusion process with open boundaries, providing explicit formulas for steady states, currents, correlations, and large deviations, and connecting microscopic results with macroscopic fluctuation theory.

Contribution

It presents a new integrable multi-species SSEP model with exact solutions for steady states, currents, correlations, and large deviations, linking microscopic and macroscopic descriptions.

Findings

Exact steady state in matrix product form

Explicit expressions for particle currents and correlations

Consistency with macroscopic fluctuation theory

Abstract

We introduce a multi-species generalization of the symmetric simple exclusion process with open boundaries. This model possesses the property of being integrable and appears as physically relevant because the boundary conditions can be interpreted as the interaction with particles reservoirs with fixed densities of each species. The system is driven out-of-equilibrium by these reservoirs. The steady state is analytically computed in a matrix product form. This algebraic structure allows us to obtain exact expressions for the mean particle currents and for the one and two-point correlation functions. An additivity principle is also derived from the matrix ansatz and permits the computation of the large deviation functional of the density profile. We also propose a description of the model in the context of the macroscopic fluctuation theory and we check the consistency with the exact computations from the finite size lattice.