Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$

TL;DR

This paper introduces the complete box-ball system (cBBS), an integrable cellular automaton linked to quantum group $U_q( ext{sl}_n)$, and studies its non-equilibrium behavior using generalized hydrodynamics, showing strong theoretical and numerical agreement.

Contribution

The paper presents the cBBS with diagonal soliton scattering and applies generalized hydrodynamics to analyze its non-equilibrium dynamics.

Findings

Excellent agreement between theory and simulation on density plateaux.

Diagonal scattering simplifies analysis compared to conventional BBS.

Thermodynamic Bethe ansatz accurately predicts non-equilibrium behavior.

Abstract

We introduce the complete box-ball system (cBBS), which is an integrable cellular automaton on 1D lattice associated with the quantum group $U_q(\widehat{sl}_n)$. Compared with the conventional $(n-1)$-color BBS, it enjoys a remarkable simplification that scattering of solitons is totally diagonal. We also submit the cBBS to randomized initial conditions and study its non-equilibrium behavior by thermodynamic Bethe ansatz and generalized hydrodynamics. Excellent agreement is demonstrated between theoretical predictions and numerical simulation on the density plateaux generated from domain wall initial conditions including their diffusive broadening.