Abstract

In this talk, I will introduce a few related microscopic models for active matter. The models we consider are lattice gases, meaning that the active particles jump stochastically on a lattice. Their active nature is represented by a drift in their stochastic jumps, whose direction can evolve in time as particles interact with eachother. I will discuss how, with this type of lattice gases, one can model the behavior of active matter, and recover the emergence of Vicsek’s alignment phase transition as well as Motility Induced Phase Separation (MIPS), both classical phenomena for active matter. Both have been well documented by the physics community, however mathematical results remain scarce. Notably, using the mathematical theory of hydrodynamic limit, one can prove the emergence of both phenomena mathematically, even for models with purely local interactions, without any mean-field type assumptions.  

Based on JW with Mourtaza Kourbane Houssène, Julien Tailleur, Thierry Bodineau, James Mason, Maria Bruna, Robert Jack