The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function
Quantum Algebra
2009-11-11 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
Vertex models with quantum group symmetry give rise to integrable cellular automata at q=0. We study a prototype example known as the periodic box-ball system. The initial value problem is solved in terms of an ultradiscrete analogue of the Riemann theta function whose period matrix originates in the Bethe ansatz at q=0.
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Cite
@article{arxiv.math/0606208,
title = {The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function},
author = {Atsuo Kuniba and Reiho Sakamoto},
journal= {arXiv preprint arXiv:math/0606208},
year = {2009}
}
Comments
11 pages, 1 figure