English

Generalized hydrodynamics in box-ball system

Mathematical Physics 2020-12-23 v2 Statistical Mechanics math.MP Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.2004.01569,
  title  = {Generalized hydrodynamics in box-ball system},
  author = {Atsuo Kuniba and Grégoire Misguich and Vincent Pasquier},
  journal= {arXiv preprint arXiv:2004.01569},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T14:38:19.210Z