Large Stochastic Dynamical Models
in Non-Equilibrium Statistical Physics
ANR project, 2016-2020
Stefano Olla (CEREMADE, Paris Dauphine)
Thierry Bodineau (CMAP, Ecole Polytechnique)
Fabio Toninelli (CNRS and Université Lyon 1)
Macroscopic transport phenomenaOne of our goals is to understand how macroscopic evolution equations arise from microscopic dynamics after a coarse graining and a proper rescaling of space and time. We are interested in the properties of the stationary non-equilibrium states. We study the corresponding transport coefficients, e.g. thermal conductivity, and the superdiffusion arising when these coefficients diverge in low dimensional systems. We also analyze the fluctuations and the large deviations around the limit macroscopic behavior.
Slow and disordered dynamicsIn some physical systems, like glasses, the dynamics are so slow that these systems never reach equilibrium within observable time scales. These dynamics play a key role in non-equilibrium physics and we study three types of models where dynamical slowdown has very different origins: geometric constraints, condensation and disorder.
Interface dynamics and KPZ equationInterface dynamics are ubiquitous in non- equilibrium statistical mechanics, in modeling the evolution of phase boundaries, growth models, etc. According to the scale one is interested in, they can be effectively described via deterministic PDEs of mean-curvature type or by (highly singular) stochastic PDEs. Both regimes pose challenging mathematical questions. Growth models are intimately related to the asymmetric lattice gases out of equilibrium.