Exclusion process for particles of arbitrary extension: Hydrodynamic limit and algebraic properties

TL;DR

This paper extends the asymmetric exclusion process to particles of arbitrary length, deriving hydrodynamic equations and algebraic properties, including the diffusion constant and symmetry generalizations.

Contribution

It introduces the $ ext{l}$-ASEP model for extended particles, deriving its hydrodynamic limit and algebraic properties, expanding understanding of exclusion processes.

Findings

Hydrodynamic equation for local density derived

Time-dependent diffusion constant calculated

SU(2)-symmetry generalized to extended particles

Abstract

The behaviour of extended particles with exclusion interaction on a one-dimensional lattice is investigated. The basic model is called $\ell$-ASEP as a generalization of the asymmetric exclusion process (ASEP) to particles of arbitrary length $\ell$. Stationary and dynamical properties of the $\ell$-ASEP with periodic boundary conditions are derived in the hydrodynamic limit from microscopic properties of the underlying stochastic many-body system. In particular, the hydrodynamic equation for the local density evolution and the time-dependent diffusion constant of a tracer particle are calculated. As a fundamental algebraic property of the symmetric exclusion process (SEP) the SU(2)-symmetry is generalized to the case of extended particles.