Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution

TL;DR

This paper provides an exact analytical solution for the vibrational spectrum of low-temperature glasses, revealing universal features and two classes of soft modes related to jamming and energy landscape structure.

Contribution

It introduces an exact analytical model of the vibrational spectrum in glasses, identifying two classes of soft modes and demonstrating universality in disordered systems.

Findings

Identification of two classes of soft modes: near jamming and throughout the glass phase.

Universal vibrational spectrum in disordered systems.

Analytical understanding of low-temperature glass vibrations.

Abstract

We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way towards a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.