## Section: New Results

### Problems in Statistical Mechanics

Participant : Stefano Olla.

S. Olla is currently developping his work in several research directions

Heat Transport in a Weakly Interacting Anharmonic Cristal, in collaboration with C. Liverani. The program is to derive the heat equation and Fourier's law of condution from microscopic hamiltonian dynamics of chains of anharmonic oscillators, in a diffusive rescaling of space and time. A preliminary result proves an autonomous dynamics for the energies of the particles in the appropriate long time scaling limit.

Work and entropy for an anharmonic chain in the hyperbolic macroscopic space-time scale, with N. Even. We study the macroscopic effect, in an hyperbolic space- time scale limit, of the application of a force at the boundary of a chain of anharmonic oscillators.

Einstein relation and linear response for a random walk in a random Galtson-Watson tree, with G. Ben Arous and O. Zeitouni. The program is to compute effective macroscopic velocities for particles in random environment driven by an external force (gravity, electric field etc.).