Obiettivo Jamming of hard spheres is a new critical phenomenon whose exponents are different from those of the other known transitions. These exponents have been recently computed in a mean field approximation whose limits of validity are not known. Even if their values are in very good agreement with the ones obtained by accurate numerical simulations, the deep reasons for this success are not understood.Trampolining from these results I plan to develop a theory of the large scale properties of the free energy landscape of glasses at low temperature. I will use techniques of statistical field theory and of renormalization group to identify and compute universal features. This proposal has the following goals.• We will develop a complete analytic theory of the infinite pressure limit (jamming) of hard spheres in dimensions greater than the upper critical dimensions. We will first compute analytically the upper critical dimension. Numerical simulations suggest that the upper critical dimensions is equal to or smaller than 2: this result is puzzling and it would be very interesting to find out if this indication is supported by the theory. We will also investigate in detail the scaling properties and the conformal invariance of the correlation functions.• Starting from these results we will derive universal properties of glassy materials in the low temperature regions in the classical and in the quantum regime. The properties of multiple equilibrium configurations are crucial; we will study the structure of small (localized or extended) oscillations around them, the classical and quantum tunneling barriers.• We will analyze both equilibrium features and off-equilibrium features (like plasticity and the time dependence of the specific heat). The subject has been widely discussed and phenomenological laws have been derived. I aim to obtain these laws from first principles using the properties of the free energy landscape in glasses that will be derived analytically. Campo scientifico natural sciencesmathematicspure mathematicsmathematical analysisfunctional equationsengineering and technologymaterials engineeringnatural sciencesphysical sciencesclassical mechanicsstatistical mechanicsnatural sciencescomputer and information sciencesartificial intelligencemachine learningdeep learningnatural sciencescomputer and information sciencesartificial intelligencecomputational intelligence Parole chiave Critical phenomena Scaling invariant theories Renormalization group Disordered systems Replica symmetry breaking Glasses Jamming Programma(i) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Argomento(i) ERC-ADG-2015 - ERC Advanced Grant Invito a presentare proposte ERC-2015-AdG Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-ADG - Advanced Grant Istituzione ospitante UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA Contribution nette de l'UE € 1 760 000,00 Indirizzo Piazzale Aldo Moro 5 00185 Roma Italia Mostra sulla mappa Regione Centro (IT) Lazio Roma Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 760 000,00 Beneficiari (1) Classifica in ordine alfabetico Classifica per Contributo netto dell'UE Espandi tutto Riduci tutto UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA Italia Contribution nette de l'UE € 1 760 000,00 Indirizzo Piazzale Aldo Moro 5 00185 Roma Mostra sulla mappa Regione Centro (IT) Lazio Roma Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 1 760 000,00