Statistical Mechanical Interpretation of the Inverse Scattering Method: Level Dynamics for Exclusion Statistics

Considered is the relationship between the level dynamics and the integrable differential-difference equation. By applying the inverse scattering method to the Bogoyavlensky lattice, which is an extension of the Volterra model, the role of the exclusion statistics is clarified. Each dynamical variable is identified with an energy level. Briefly discussed is a generalization of the Yangian symmetric system, and the “Gentile” statistics is revealed.