Exact dynamical correlations of the 1/r² model

Abstract

We present exact results for the dynamical structure function, i.e., the density-density correlations for the 1/r² system of interacting particles at three special values of the coupling constant. The results are interpreted in terms of exact excitations of the model which are available from Bethe's Ansatz, thereby throwing light on the quasiparticle content of the elementary excitations. We also obtain the first moment of the discrete version of the model, which provides a nontrivial check on its structure function. We show that the property of spectrum saturation is a common feature of both versions.