Correlation functions and dynamics in quantum integrable model

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Using Bethe ansatz method, we clarified the dynamical properties of the integrable model---one dimensional spinless fermion model and Heisenberg model. In particular, the properties in the high-energy region are elucidated from the analysis of the string states. Further, we obtained the particle propagator of the Ruijsenaars-Schneider model and clarified the dynamical properties in terms of the excitations obeying fractional statistics. We show the mutual equivalence among the known several expressions of the density matrix for the Gutzwiller wave function exactly.