Non-equilibrium fluctuations in open quantum systems

01.01.2022 bis 31.12.2023

The research proposal regards a very active area of current theoretical physics, which is non-equilibrium quantum statistical mechanics. The equilibrium thermodynamics of systems composed by many constituents, e.g. a gas, is known since two centuries in terms of statistical mechanics, as pioneered by Boltzmann. For out equilibrium systems, on the contrary, very few general principles are known. The quest for a general framework to encompass non-equilibrium processes is therefore timely and of paramount importance, as the understanding of these phenomena might pave the way for the discovery of new states of non-equilibrium quantum matter and materials. To address this issue, in the research proposal, the Fellow consider a very important non-equilibrium protocol with ubiquitous technological applications, i.e. many body quantum systems supporting the flow of a current, for instance of energy or particle. Two main tools for my analysis will then be used. The first is the large deviation approach, which is a general theory to study large, atypical, fluctuations of the current from the average value. The second is ”hydrodynamics”, i.e. a large scale - zoomed out - description where one considers the individual particles constituting the system as a continuum fluid. The main goal of the research proposal is then to derive this hydrodynamic description for out of equilibrium open, i.e. coupled to the external environment, quantum systems admitting anomalous transport. The latter refers to situations when transport occurs because of a different mechanics than the typical diffusion processes. In parallel, in the proposal the Fellow will develop a deeper understanding of dynamical phase transitions, which correspond to dramatic changes in the way the system evolves in time. The development of such general techniques will have a tremendous impact as universally applicable approaches to study out of equilibrium systems are extremely scarce. Moreover, these methods are fundamental at the technological level as they will allow to develop new techniques that enable the discovery and classification of novel, dynamical, forms of matter and exotic materials.