Energy Functions in Box Ball Systems

Abstract

The box ball system is studied in the crystal theory formulation. New conserved quantities and the phase shift of the soliton scattering are obtained by considering the energy function (or $H$-function) in the combinatorial $R$-matrix.

15 pages, LaTeX2e: one paragraph replaced and reference added in Introduction, a paragraph added in Section 2.5, remark 2) after Th 4.6 added

Cited by in corpus (39)

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• Box ball system associated with antisymmetric tensor crystals
• Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
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• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
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• Box-Basket-Ball Systems
• Stable Rigged Configurations for Quantum Affine Algebras of Nonexceptional Types
• Noncommutative Schur polynomials and the crystal limit of the U_q sl(2)-vertex model
• Combinatorial R-matrices for Kirillov--Reshetikhin crystals of type D^{(1)}_n, B^{(1)}_n, A^{(2)}_{2n-1}
• Combinatorial Bethe ansatz and generalized periodic box-ball system
• A Quantization of Box-Ball Systems
• A uniform approach to soliton cellular automata using rigged configurations
• Generalized hydrodynamics in complete box-ball system for $U_q({\widehat{sl}}_n)$
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• Commuting Time Evolutions in the Tropical Periodic Toda Lattice
• Geometric lifting of the integrable cellular automata with periodic boundary conditions
• Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$
• Correlation function for a periodic box-ball system
• Scaling limit of soliton lengths in a multicolor box-ball system
• Creation of ballot sequences in a periodic cellular automaton
• A crystal theoretic method for finding rigged configurations from paths
• Differential equations for the closed geometric crystal chains
• Soliton cellular automata for the affine general linear Lie superalgebra