D1 - Conoscenza e capacità di comprensione

Learn the phenomenology of liquids, supercooled liquids, structural glasses, spin glasses, as well as the main concepts and theoretical models to describe their physical properties

D2 - Capacità di applicare conoscenza e comprensione

Identify the appropriate theoretical models to describe a disordered system, reproduce the analytical predictions of simple theoretical models, critically assess these predictions for the system of interest, describe and analyze the predictions of more complex theories

D3 - Autonomia di giudizio

Identify the limitations and approximations involved in the theoretical models described in the course

D4 - Abilità comunicative

Describe the contents of the course using appropriate language

D5 - Capacità di apprendimento

Delve deeper into the subject matter of the course by reading research articles and/or execution of computaional notebooks, also in connection with outstanding problems related to glass science and soft matter

Thermodynamics, statistical physics

The goal of the course is to introduce the students to the phenomenology and theoretical description of disordered systems, focusing on the physical properties of liquids, structural glasses and spin glasses. The course will provide the students with the concepts and mathematical tools needed to model such systems. It will also introduce some of the outstanding problems in the physics of disordered systems. Same aspects will be investigated with a numerical approach. - Introduction: kinds of disorder, order and broken symmetries, short-, medium- and long-range correlations, order and dimensionality, hard and soft matter, elastic moduli and viscosity, visco-elastictity - Brownian dynamics: physical examples, Langevin equation, fluctuation-dissipation relation, over-damped limit, Smoluchowski equation, thermal activation - Liquids: transport phenomena, static and dynamic correlation functions, linear response , fluctuation-dissipation theorem, response functions, Green-Kubo relations, density-density dynamic correlation functions, free regime, hydrodynamic limit, Gaussian approximation, memory functions - Supercooled liquids and glasses: metastable and unstable fluids, classical nucleation theory, spinodal decomposition, glass transition: timescales, time-temperature-transformation diagram, Angell classification, configurational entropy and Kauzmann paradox, Adam-Gibbs model, energy landscape, predictions of mode-coupling theory, models for the structure of glasses - Spin glasses: phenomenology of spin glass and theoretical models, Edwards-Anderson order parameter, replica method, mean-field theory for the Sherrington-Kirkpatrick model, replica symmetry breaking, p-spin models and connection with mode-coupling theory, random first-order transition theory

- "Basic concepts for simple and complex liquids", Jean-Louis Barrat, Jean-Pierre Hansen

- "Theory of simple liquids", Jean-Pierre Hansen, Ian R. Mc Donald

- "Glassy materials and disordered solids: an introduction to their statistical mechanics", Kurt Binder, Walter Kob

- "Physics of Liquid Matter", Paola Gallo, Mauro Rovere

- Introduction: kinds of disorder, order and broken symmetries, short-, medium- and long-range correlations, order and dimensionality, hard and soft matter, elastic moduli and viscosity, visco-elastictity - Brownian dynamics: physical examples, Langevin equation, fluctuation-dissipation relation, over-damped limit, Smoluchowski equation, thermal activation - Liquids: transport phenomena, static and dynamic correlation functions, linear response , fluctuation-dissipation theorem, response functions, Green-Kubo relations, density-density dynamic correlation functions, free regime, hydrodynamic limit, Gaussian approximation, memory functions - Supercooled liquids and glasses: metastable and unstable fluids, classical nucleation theory, spinodal decomposition, glass transition: timescales, time-temperature-transformation diagram, Angell classification, configurational entropy and Kauzmann paradox, Adam-Gibbs model, energy landscape, predictions of mode-coupling theory, models for the structure of glasses - Spin glasses: phenomenology of spin glass and theoretical models, Edwards-Anderson order parameter, replica method, mean-field theory for the Sherrington-Kirkpatrick model, replica symmetry breaking, p-spin models and connection with mode-coupling theory, random first-order transition theory.

Lectures. Some aspects of the subject matter will be investigated using a numerical approach, through jupyter notebooks. The students will be encouraged to read autonomously research articles related to the subject matter.

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Oral exam (maximum grade 30 e lode). One question will focus on an exercise or jupyter notebook chosen by the student among those made available by the teacher. An additional question will be chosen by the teacher. To pass the exam, the student must: (I) demonstrate a solid knowledge of the physical concepts and theoretical tools presented in the course; (ii) be able to illustrate clearly and precisely their application to the modeling of a disordered system; (iii) be able to identify connections between the different topics presented in the course. Each of the goals identified above will contribute equally to the final mark. The exams may be held in Italian or English, at the student's choice.