Periodic cellular automata and Bethe ansatz
Mathematical Physics
2012-09-04 v3 math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
We review and generalize the recent progress in a soliton cellular automaton known as the periodic box-ball system. It has the extended affine Weyl group symmetry and admits the commuting transfer matrix method and the Bethe ansatz at q=0. Explicit formulas are proposed for the dynamical period and the number of states characterized by conserved quantities.
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Cite
@article{arxiv.math-ph/0511013,
title = {Periodic cellular automata and Bethe ansatz},
author = {Atsuo Kuniba and Akira Takenouchi},
journal= {arXiv preprint arXiv:math-ph/0511013},
year = {2012}
}
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8 pages