A Quantization of Box-Ball Systems

Abstract

An L operator is presented related to an infinite dimensional limit of the fusion R matrices for U_q(A^{(1)}_{n-1}) and U_q(D^{(1)}_n). It is factorized into the local propagation operators which quantize the deterministic dynamics of particles and antiparticles in the soliton cellular automata known as the box-ball systems and their generalizations. Some properties of the dynamical amplitudes are also investigated.

29 pages, 8 figures

References in corpus (6)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Soliton Cellular Automata Associated With Crystal Bases
• Energy Functions in Box Ball Systems
• Simple Algorithm for Factorized Dynamics of g_n-Automaton
• Factorization of Combinatorial R matrices and Associated Cellular Automata
• Tropical R and Tau Functions

Cited by in corpus (4)

• Matrix product formula for Macdonald polynomials
• Soliton decomposition of the Box-Ball System
• A note on $q$-oscillator realizations of $U_q(gl(M|N))$ for Baxter $Q$-operators
• Bethe ansatz at q=0 and periodic box-ball systems