Periodic cellular automata and Bethe ansatz
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2005
- DOI:
- 10.48550/arXiv.math-ph/0511013
- arXiv:
- arXiv:math-ph/0511013
- Bibcode:
- 2005math.ph..11013K
- Keywords:
-
- Mathematical Physics;
- Mathematics - Quantum Algebra;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 8 pages