## Quantum Mechanics

We aim to develop new mathematically rigorous methods to investigate quantum many-body systems at- and near equilibrium.

This line of research also includes studies of quantum dynamics and transport properties in random media as well as the challenging future application of quantum technologies related to simulations of Dirac equation and Bose-Einstein condensation in ultra-cold gases. It is at the interface between mathematics (convex analysis, functional analysis, random processes, operator algebras, non-autonomous evolution equations, rigorous renormalization group, PDE) and quantum physics (transport properties, lasers, superconductivity, BEC, etc.).

*Understand how the same microscopic laws yield a large number of thermodynamic behaviors*