STAGE Flow Equation Approaches for Disordered Quantum Systems Out of Equilibrium

Quenched random disorder can have dramatic effects on transport and dynamical properties of quantum many-body systems, leading to a complete breakdown of diffusion and to the localized non-ergodic behavior of a non-interacting quantum particle in a random external potential, as first predicted by Anderson. For long times it was thought that such a localized phase would have not survived in presence of finite interaction and finite excitation energy(temperature); the recent theoretical and experimental discovery of Many Body Localization (MBL) therefore came as a surprise. MBL is a new quantum phase of matter where thermalization and equilibration break down due to strong disorder, resulting in a number of remarkable non equilibrium properties. We have recently developed a flow-equation approach to describe static and dynamical properties of MBL phases and the goal of this master project is to use and extend further this technique to different settings, including generic time dependent problems, periodically driven systems, dissipative systems.