Interacting non integrable quantum many body systems are expected to reach thermal equilibrium when isolated from their environment and let evolve under their own quantum dynamics. Exceptions to this paradigm can emerge in presence of quenched random disorder, due to many body localization (MBL) or quantum glassiness. Those two robust scenarios for ergodicity breaking have recently attracted considerable interest both from a purely theoretical viewpoint and for their implications on the robustness of future quantum technologies. In this talk I will study the quantum dynamics of prototype models for MBL and quantum glassy systems. I will first introduce a theoretical framework based on flow equations to study the properties MBL systems, in particular the emergence of localised integral of motions, and their dynamics. Then I will consider a model of quantum glass and study its isolated dynamics after a quantum quench. I will show that, contrary to the conventional wisdom based on thermodynamics, quantum fluctuations and non equilibrium effects result in enhanced glassiness and ageing behavior.
Fluid flows can induce long-ranged interactions and propagate information on large scales. Especially during the development of an organism, coordination on large scales is essential. What are the principal mechanisms of how fluid flows induce, transmit and respond to biological signals and thus control morphology? Fluid flows are particularly prominent during the growth and adaptation of transport networks. Here, the network-forming slime mold Physarum polycephalum emerged as a model system. Investigating the pivotal role of fluid flows in this live transport network we find that flows are patterned in a peristaltic wave across the network thereby optimizing transport. In fact, flows are hijacked by signals to propagate throughout the network. This simple mechanism is sufficient to explain surprisingly complex dynamics of the organism like scaling of peristaltic wave with network size and finding the shortest path through a maze.
Developing a theory of activated dynamics is one of the most challenging problems of disordered systems. Activated glassy dynamics is central in many different contexts both in physics and beyond, e.g. in computer science and biology. In this talk, after a general introduction, I will describe recent research works aimed at characterising the activated dynamics of mean-field glassy systems. In particular I will discuss numerical results on the random energy model and variants, and analytical results on the organization of barriers in the p-spin spherical model.