"The topic of this project is the theoretical understanding of quantum systems involving a large number of interacting degrees of freedom. In general, systems of this kind exhibit chaotic dynamics which brings them to thermal equilibrium, where the state is completely described by the temperature. Here, we focus to the situation where the system is perturbed by the presence of an external drive. In particular, settings where the drive strength can be considered weak are important because they lead to a separation of time scale: because of its intrinsic chaotic dynamics, the system is capable of thermalising and it reaches an equilibrium state; however because of the weak drive, the equilibrium state slowly changes in time. This ""quasi-equilibrium"" regime allows for an effective and controlled treatment because only the dynamics of a few parameters (generalized temperatures conjugated to the conserved quantities) has to be taken into account.
Novel phases of matter can emerge at large times by engineering experimental setups where the competition between the tendency toward equilibrium of the system itself and the drive result in interesting physical phenomena (long-range order, cooling effects, etc). An important example considered in detail is dynamic nuclear polarization (DNP), with promising application for medical imaging. DNP is a protocol used in nuclear magnetic resonance (NMR) to increase the nuclear polarization in a compound doped doped with unpaired electron spins. The compound is driven by turning on a microwave irradiation: then, the interacting spin system of electrons and nuclei reorganizes itself in an out-of-equilibrium steady state characterized by an enhanced nuclear polarization, due to an extremely low effective temperature. This setup emerges exactly in the regime of weak dissipation/drive at the centre of this programme.
As a second important aspect, we focus on those effects which can prevent the emergence of chaotic dynamics. This phenomenon is named ""many-body localization"" (MBL) as it signals the tendency of the system to remain stuck close to its initial configuration. It is possible in a quantum setup in the presence of strong disorder and sufficiently weak interactions. MBL was theoretically conjectured in the last ten years and has received experimental confirmation. In this case, we consider the effect of a weak drive on a system which becomes less and less chaotic because of the presence of many-body localization. The combination of MBL and a drive is at the origin of the intriguing mechanism of time crystals, but further technological applications (quantum memory, quantum computation, etc.) can be imagined in the near future.
Aim of this programme is therefore to reach a full theoretical understanding of disordered weakly driven/dissipative systems, providing clear experimental signatures of MBL and increasing the control in the ergodic phase for applications."
