Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids
Andrea Cavagna, Irene Giardina, Giorgio Parisi
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.
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