Francesco Zamponi, ENS Paris, France
Theory of the glass and jamming transitions in infinite dimensions
1. Atomic liquids in infinite dimensions, thermodynamics:
Basic observables, the virial expansion, virial expansion in large
dimensions, hard spheres and other potentials.
2. Atomic liquids in infinite dimensions,
equilibrium liquid dynamics:
Models of equilibrium dynamics, basic observables, self-consistent
dynamical mean field equations, properties of the liquid phase.
3. Atomic liquids in infinite dimensions,
Dynamical glass transition, calculation of the plateau of dynamical
correlations, critical properties of the dynamical transition.
4. State following: Replica symmetric results:
the Franz-Parisi construction, calculation of the Franz-Parisi free
energy in infinite dimensions, replica symmetry, phase diagram of
thermal glasses, phase diagram of hard sphere glasses: glass vs
5. Complexity: Replica symmetric results,
equilibrium complexity, out-of-equilibrium complexity, the Monasson
method, phase diagram, connection with the Edwards ensemble for hard
spheres, protocol dependence of the jamming transition.
6. Elements of replica symmetry breaking:
Hierarchical free energy landscapes, an introduction to replica
symmetry breaking, equations for the Gardner transition, replica
symmetry breaking phase diagram, critical exponents for the jamming
7. Discussion and closing remarks.