Exact pair correlation of the one-dimensional quantum gas with 1/${\mathit{r}}^2$ repulsion derived from the sympletic Dyson ensemble

The spectra of nonintegrable or quantum chaotic systems with unitary or orthogonal symmetry were recently shown to display universality in the response of energy levels to arbitrary perturbations. We show that this type of universality extends to symplectic ensembles. In doing so, we obtain an exact expression for the autocorrelator of particle density fluctuations of a system of one-dimensional particles interacting through a repulsive 1/${\mathit{r}}^2$ pairwise potential.