A new approach for the analytic computation of the Instantaneous Normal Modes spectrum

TL;DR

This paper introduces a novel analytical method for computing the Hessian spectrum in the Instantaneous Normal Mode approach, specifically applied to low-density one-dimensional systems with repulsive interactions, enhancing theoretical understanding of liquid behavior.

Contribution

It presents a new analytical technique for calculating the Hessian spectrum in the INM framework, with exact results for 1D low-density repulsive particle systems.

Findings

Exact spectrum computation for 1D low-density systems

Comparison with existing methods shows advantages

Method extension potential discussed

Abstract

In the context of the Instantaneous Normal Mode approach, the spectrum of the Hessian of Hamiltonian is a key quantity to describe liquids behaviour. The determination of the spectrum represents a major task for theoretical studies, and has been addressed recently in various works. In this paper a new approach for the analytic computation of the Hessian spectrum is presented. The one dimensional case for a system of particles interacting via a purely repulsive potential at low density is analyzed in details and the spectrum is computed exactly also in the localized sector. Finally, the possible extensions of the method are discussed, together with a comparison with different approaches to the problem.