Dynamics of Disordered Systems

A generic quantum many body system, initialised to a typical state, forgets the memory of the initial state. In the long time limit, local observables in the system can be described by an ensemble of states with a probability measure determined by its Hamiltonian. This basic tenet of equilibrium statistical mechanics has been challenged in recent years in strongly disordered interacting quantum systems, a phenomenon called many body localization. Theoretical studies on many-body localization (MBL) in disordered systems have mostly focused on the properties of the many-body eigenstates in equilibrium. Following experimental protocol to detect evidences of MBL in ultracold atomic experiments, we are interested in studying the longtime dynamics of the disordered (quasi-periodic) system. The system is initially imprinted (as shown in the figure) with a finite density imbalance on lattice and the presence of a finite imbalance in the long-time dynamics signals that the system retains initial memory and fails to thermalise. Even though MBL is a well-studied topic, it is still a highly debated field regarding the stability of the MBL phase. Using non-equilibrium field theory formulation which can keep track of memory of non-thermal initial conditions, we plan to investigate  the stability of the MBL phase against quantum avalanches. We plan to investigate (a) does the many-body ‘near resonances’ lead to decay of initial memory in the noise correlators? (b) If it leads to a prethermal region, what is the microscopic mechanism behind that?