Exact Dynamical Correlations of the 1/r^2 Model

TL;DR

This paper derives exact dynamical correlation functions for the 1/r^2 interacting particle model at specific couplings, using Bethe's Ansatz to elucidate its quasi-particle excitations and spectrum properties.

Contribution

It provides the first exact dynamical structure function for the 1/r^2 model at special couplings, linking excitations to Bethe's Ansatz and spectrum saturation.

Findings

Exact dynamical structure functions obtained at three coupling values.

Identification of elementary excitations via Bethe's Ansatz.

Spectrum saturation observed in both continuous and discrete models.

Abstract

We present exact results for the dynamical structure function, i.e.~the density-density correlations for the 1/r^2 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 quasi-particle content of the elementary excitations. We also obtain the first moment of the discrete version of the model, which provides a non-trivial check on its structure function. We show that the property of spectrum saturation is a common feature of both versions.