We analytically compute the spectrum of the Hessian of the Hamiltonian for a system of $N$ particles interacting via a purely repulsive potential in one dimension. Our approach is valid in the low-density regime, where we compute the exact spectrum also in the localized sector. We finally perform a numerical analysis of the localization properties of the eigenfunctions.

• Received 11 March 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.108