Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 027, 16 pages      arXiv:1103.3929
Contribution to the Proceedings of the Conference “Integrable Systems and Geometry”

Two Point Correlation Functions for a Periodic Box-Ball System

Jun Mada a and Tetsuji Tokihiro b
a) College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba 275-8576, Japan
b) Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan

Received December 13, 2010, in final form March 02, 2011; Published online March 21, 2011

We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific N-point functions is also presented.

Key words: correlation function; box-ball system.

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  1. Takahashi D., Satsuma J., A soliton cellular automaton, J. Phys. Soc. Japan 59 (1990), 3514-3519.
  2. Yura F., Tokihiro T., On a periodic soliton cellular automaton, J. Phys. A: Math. Gen. 35 (2002), 3787-3801, nlin.SI/0112041.
  3. Fukuda K., Okado M., Yamada Y., Energy functions in box ball systems, Internat. J. Modern Phys. A 15 (2000), 1379-1392, math.QA/9908116.
  4. Hatayama G., Hikami K., Inoue R., Kuniba A., Takagi T., Tokihiro T., The AM(1) automata related to crystals of symmetric tensors, J. Math. Phys. 42 (2001), 274-308, math.QA/9912209.
  5. Mada J., Tokihiro T., Correlation functions for a periodic box-ball system, J. Phys. A: Math. Theor. 43 (2010), 135205, 15 pages, arXiv:0911.3953.
  6. Jimbo M., Miwa T., Quantum KZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime, J. Phys. A: Math. Gen. 29 (1996), 2923-2958.
  7. Mada J., Idzumi M., Tokihiro T., The exact correspondence between conserved quantities of a periodic box-ball system and string solutions of the Bethe ansatz equations, J. Math. Phys. 47 (2006), 053507, 18 pages.
  8. Torii M., Takahashi D., Satsuma J., Combinatorial representation of invariants of a soliton cellular automaton, Phys. D 92 (1990), 209-220.

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