# Generalized hydrodynamics in box-ball system

@article{Kuniba2020GeneralizedHI, title={Generalized hydrodynamics in box-ball system}, author={Atsuo Kuniba and Gr'egoire Misguich and Vincent Pasquier}, journal={arXiv: Mathematical Physics}, year={2020} }

Box-ball system (BBS) is a prominent example of integrable cellular automata in one dimension connected to quantum groups, Bethe ansatz, ultradiscretization, tropical geometry and so forth. In this paper we study the generalized Gibbs ensemble of BBS soliton gas by thermodynamic Bethe ansatz and generalized hydrodynamics. The results include the solution to the speed equation for solitons, an intriguing connection of the effective speed with the period matrix of the tropical Riemann theta…

## 12 Citations

Generalized Hydrodynamic Limit for the Box–Ball System

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2020

We deduce a generalized hydrodynamic limit for the box-ball system, which explains how the densities of solitons of different sizes evolve asymptotically under Euler space-time scaling. To describe…

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

- Physics
- 2020

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…

Generalized hydrodynamics in complete box-ball system for U q ( Ò sl n )

- Physics
- 2021

We introduce the complete box-ball system (cBBS), which is an integrable cellular automaton on 1D lattice associated with the quantum group Uq( sln). Compared with the conventional (n − 1)-color BBS,…

Current correlations, Drude weights and large deviations in a box-ball system

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2022

We explore several aspects of the current fluctuations and correlations in the box-ball system (BBS), an integrable cellular automaton in one space dimension. The state we consider is an ensemble…

Sub-lattice entanglement in an exactly solvable anyon-like spin ladder

- Physics
- 2022

We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd…

A Yang–Baxter integrable cellular automaton with a four site update rule

- Computer Science
- 2021

A one dimensional reversible block cellular automaton, where the time evolution is dictated by a period 3 cycle of update rules, which embeds the model into the canonical framework of Yang–Baxter integrability by rigorously proving the existence of a commuting set of diagonal-to-diagonal transfer matrices.

Anisotropic Landau-Lifshitz model in discrete space-time

- PhysicsSciPost Physics
- 2021

We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of
the lattice Landau-Lifshitz ferromagnet with uniaxial…

Form factors and generalized hydrodynamics for integrable systems

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

Our review covers microscopic foundations of generalized hydrodynamics (GHD). As one generic approach we develop form factor expansions, for ground states and generalized Gibbs ensembles (GGE). In…

Integrable spin chains and cellular automata with medium-range interaction

- PhysicsPhysical Review E
- 2021

We study integrable spin chains and quantum and classical cellular automata with interaction range ` ≥ 3. This is a family of integrable models for which there was no general theory so far. We…

Soliton Decomposition of the Box-Ball System

- MathematicsForum of Mathematics, Sigma
- 2021

Abstract The box-ball system (BBS) was introduced by Takahashi and Satsuma as a discrete counterpart of the Korteweg-de Vries equation. Both systems exhibit solitons whose shape and speed are…

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