K. Hikami, STATISTICAL-MECHANICAL INTERPRETATION OF THE INVERSE SCATTERING METHOD - LEVEL DYNAMICS FOR EXCLUSION STATISTICS, Physical review letters, 80(20), 1998, pp. 4374-4377
Considered is the relationship between the level dynamics and the inte
grable differential-difference equation. By applying the inverse scatt
ering method to the Bogoyavlensky lattice, which is an extension of th
e Volterra model, the role of the exclusion statistics is clarified. E
ach dynamical variable is identified with an energy level. Briefly dis
cussed is a generalization of the Yangian symmetric system, and the ''
Gentile'' statistics is revealed.