A new approach for the analytic computation of the instantaneous normalmodes spectrum

Abstract

In the context of the instantaneous normal mode approach, the spectrum of theHessian of Hamiltonian is a key quantity to describe a liquids behaviour. Thedetermination of the spectrum represents a major task for theoretical studies,and has recently been addressed in various works. In this work a new approachfor the analytic computation of the Hessian spectrum is presented. Theone-dimensional case for a system of particles interacting via a purelyrepulsive potential at low density is analysed in detail and, also in thelocalized sector, the spectrum is computed exactly. Finally the possibleextensions of the method are discussed, together with a comparison withdifferent approaches to the problem.