Nonergodic hydrodynamics in quantum systems

forthcoming

The Universe is a non-equilibrium system that cannot be fully understood by solely thermodynamics. Quantum many-body physics has emerged as a key field for exploring fundamental questions of cosmology, statistical physics, and condensed matter, serving as the foundation for the development of future quantum technologies. Contemporary experiments probe far-from-equilibrium metastable phases and realize different instances of nonergodic systems. The breakdown of canonical thermodynamics compels a reassessment of our understanding of emergent macroscopic properties of matter. Simultaneously, strong interactions and quantum effects limit conventional numerical methods to small scales or early times. The dynamics of nonergodic systems at large scale remain an underexplored frontier that demands urgent attention. The project NonErgHydro takes on the ambitious challenge of investigating nonergodic quantum systems at the macroscopic scale. NonErgHydro renounces to postulate thermodynamics and seeks to uncover how macroscopic physics emerges from the microscopic degrees of freedom. The project will extend the concepts of hydrodynamics to non-ergodic systems identifying novel phases of matter, new transport universality classes, and providing at the same time a long-sought computational framework able to supersede conventional numerical methods, by capturing quantum effects in non-linear classical hydrodynamic equations. The accomplishment of this project will significantly advance our understanding of many-body quantum systems, by answering fundamental questions in hydrodynamics and universality. NonErgHydro seeks immediate confrontation with experiments, which will benefit from the ground-breaking methodology developed by my research team and will provide new inspiration for exciting developments.