Generalized hydrodynamics in box-ball system

Abstract

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 function, an explicit description of the density plateaux that emerge from domain wall initial conditions including their diffusive corrections.

42 pages, 9 figures. v2: New equation (5.69) and minor changes

References in corpus (2)

• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Bethe ansatz and inverse scattering transform in a periodic box-ball system

Cited by in corpus (15)

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• Hydrodynamic Equations for the Toda Lattice
• Anisotropic Landau-Lifshitz Model in Discrete Space-Time
• Current correlations, Drude weights and large deviations in a box-ball system
• Integrable spin chains and cellular automata with medium range interaction
• Finite temperature spin diffusion in the Hubbard model in the strong coupling limit
• Thermalization and hydrodynamics in an interacting integrable system: the case of hard rods
• Generalized hydrodynamics in complete box-ball system for $U_q({\widehat{sl}}_n)$
• Hydrodynamic fluctuations of stochastic charged cellular automata
• Integrable fishnet circuits and Brownian solitons