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

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.

60 pages, 10 figures. Submitted to SciPost. v2: added 2 references, order of figures changed, various other minor changes

References in corpus (6)

• Lecture notes on Generalised Hydrodynamics
• Diffusion in deterministic interacting lattice systems
• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• Generalized hydrodynamics in box-ball system
• Kirillov--Schilling--Shimozono bijection as energy functions of crystals
• Generalized hydrodynamic limit for the box-ball system

Cited by in corpus (2)

• Anisotropic Landau-Lifshitz Model in Discrete Space-Time
• Current correlations, Drude weights and large deviations in a box-ball system