Tropical spectral curves and integrable cellular automata

Details Tropical spectral curves and integrable cellular automata Tropical spectral curves and integrable cellular automata

2007-04-19

arxiv.org/abs/0704.2471v2

Physics

Mathematical Physics

22 pages

Scientific paper

We propose a method to study the integrable cellular automata with periodic boundary conditions, via the tropical spectral curve and its Jacobian. We introduce the tropical version of eigenvector map from the isolevel set to a divisor class on the tropical hyperelliptic curve. We also provide some conjectures related to the divisor class and the Jacobian. Finally, we apply our method to the periodic box and ball system and clarify the algebro-geometrical meaning of the real torus introduced for its initial value problem.

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