Statistical Physics of Disordered Systems
This course deals with systems in which the presence of impurities or amorphous structures (in other words, of disorder) influences radically the physics, generating novel phenomena. These phenomena involve the properties of the system at equilibrium (freezing and glass transitions), as well as their dynamical evolution out-of-equilibrium (pinning, avalanches), giving rise to ergodicity breaking both in absence and in presence of quantum fluctuations (classical metastability, quantum localization).
We discuss the main statistical physics models that are able to capture the phenomenology of these systems, as well as the powerful theoretical tools (replica theory, large deviations, random matrix theory, strong-disorder expansions) that have been developed to characterize quantitatively their physics, which nowadays have a huge impact in a variety of fields that go well-beyond statistical physics (computer science, probability, condensed matter, theoretical biology).
- Introduction to disordered systems. The simplest spin-glass: solution of the Random Energy Model.
- The replica method: the solution of the spherical p-spin model (1 RSB). Interface growth.
- Directed polymers in random media: the KPZ universality class.
- Scenarios for the glass transition: sketch of the solution of Sherrington Kirkpatrick model (full RSB); the glass transition in KPZ in 3D.
- Towards glassy dynamics: rugged landscapes, the trap model.
- Depinning and avalanches.
- Bienaimé-Galton-Watson processes. Anderson localization in 1D.
- Anderson model on the Bethe lattice, and links to the directed polymer problem.
- Quantum thermalization and many-body localization.
The students have two possibilities:
- A final written exam which counts for the total grade.
- An homework assignement + a written exam. The final grade is given by a weighted average of the two grades (the homework counts 1/4 and the written exam 3/4).
The course is mainly aimed at students with a background in physics. However students in chemestry or mathematics are more than welcome. A basic knowledge of statistical physics or of probability/statics is useful.
