Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids

Abstract

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.

4 RevTeX pages, 4 EPS figures. Revised version to appear on Phys. Rev. Lett

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