Disordered systems and multidisciplinary applications of statistical physics

Disordered systems and multidisciplinary applications of statistical physics

Disordered Systems – Disordered systems arise naturally in condensed matter physics. Amorphous materials such as glasses and spin glasses are examples. At IPhT, a major research activity aims to understand the nature and properties of amorphous solids at low temperatures by combining the resolution of infinite-dimensional glass models, numerical simulations and experiments. Interesting models include for example colloidal and granular systems, hard spheres as well as non-spherical particle models. The rheology of amorphous solids is also studied by developing theoretical approaches to describe the elastic transition. Another topic is the study of low energy excitations of amorphous systems. Finally, large deviation theory is used to describe typical and rare events that occur at different spatial and temporal scales in disordered systems. Example applications include glassy phases in random trap models, inference from long random walks in disordered media, kinetically constrained models, or finite-sized Lyapunov exponents in Anderson localization models .

Interdisciplinary applications of statistical physics – Theoretical tools rooted in the physics of disordered systems are applied to high-dimensional optimization problems. One line of research aims to understand the properties of gradient descent-based optimization algorithms for solving high-dimensional inference problems. At the same time, dynamic mean-field theory is being used to study the stochastic gradient descent algorithm, which is a central method in the field of deep learning. This enables us to compare the performance of this algorithm in typical high-dimensional non-convex optimization contexts. Optimal transport problems and their links to computational problems are studied using statistical physics methods. Applications of statistical physics to biophysical problems are also investigated. In addition, theoretical and algorithmic approaches are developed to study the structure of proteins and the transition paths between their states. The tools of disordered systems are also applied to the study of learning strategies in recurrent neural networks and, more generally, in high-dimensional chaotic systems. Finally, a line of research is being developed to describe the growth of cities using theoretical tools from statistical physics and stochastic processes.

Scientific staff

Marc BARTHELEMY
Pierfrancesco URBANI
Cecile MONTHUS
Henri ORLAND
Jean-Marc LUCK
Claude GODRÈCHE
Bertrand DUPLANTIER
Laura FOINI