Disorder and randomness can induce very deep complexity for systems. This project studies the importance of this induced complexity on the time evolution of such systems. It thus addresses topics at the interface between mathematics and statistical physics of disordered media. The signature of complexity on the dynamics of these complex systems is seen in the fact that the evolution is very slow and trapped in regions far from equilibrium. It exhibits new characteristics like aging, and break the well established rules of fluctuation-dissipation. Nevertheless some universal features are shared by these complex systems and this project builds the foundations for understanding these universal phenomena.
This universal behavior is exhibited in very different models which include the slow dynamics of Spin glasses, both for spherical and Ising spins, and the diffusion and transport on disordered structures like percolation clusters and random trees. One of the tools recently built (by the PI) is a new and powerful link between the study of the random energy landscapes and random matrix theory. This link will also be explored further since it enables the introduction of a new classification of different classes of complex behavior in one class of systems (the spherical spin glasses).
