title: Universal spectrum of normal modes in low-temperature glasses.
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 toward a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques (Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8626), Université de Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France; silvio.franz@lptms.u-psud.fr.
authors.forename: Silvio
authors.initials: S
authors.lastname: Franz
authors.affiliation: Dipartimento di Fisica, Sapienza Università di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, Istituto per i Processi Chimico-Fisici-Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy;
authors.forename: Giorgio
authors.initials: G
authors.lastname: Parisi
authors.affiliation: Institut de Physique Théorique, Université Paris Saclay, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Centre National de la Recherche Scientifique (CNRS), F-91191 Gif-sur-Yvette Cedex, France;
authors.forename: Pierfrancesco
authors.initials: P
authors.lastname: Urbani
authors.affiliation: Laboratoire de Physique Théorique, Ecole Normale Supérieure, Unité Mixte de Recherche 8549 Centre National de la Recherche Scientifique, 75005, France.
authors.forename: Francesco
authors.initials: F
authors.lastname: Zamponi
keywords: boson peak; glasses; jamming; normal modes