from Generalised hydrodynamics to new Effective descriptions of NonEquilibrium quantum SYStems

Understanding the out-of-equilibrium dynamics of many-body quantum systems is one of the main challenges of the Physics of the 21st century.

Despite the complexity of the field, significant steps forward have been achieved thanks to the parallel development of advanced theoretical tools, numerical methods and experimental verifications made with ultracold atoms and ions.

In this context, Generalised Hydrodynamics (GHD) represented a fundamental breakthrough which permitted the use of new integrability-based techniques to include previously untreatable experimental effects such as spatial inhomogeneities and temperature gradients.

But from this milestone, new questions inevitably arise for which the proposed action stands as a targeted plan of investigation. On the one hand, a known weakness of any hydrodynamic approach is the loss of long-range quantum fluctuations.

Although a few attempts to include quantum effects in the formulation of GHD are present, a definitive answer to this problem is still far.

On the other hand, the advent of GHD indirectly revived the interest in diffusive models, with the ultimate goal of developing a quantum analogue of the celebrated Macroscopic Fluctuations Theory.

In detail, by combining analytical and numerical methods, the proposal aims the fulfilment of three objectives within this landscape, consisting of research and training activities dedicated to i) investigating the quantum corrections of GHD and clarifying the connections among the available theories, aiming at a single description of quantum ballistic transport ii) exploit the developments in quantum ballistic transport to describe currently feasible measures of the correlations of quantum gases out-of-equilibrium iii) connect ballistic to diffusive quantum transport, starting from simple settings.

Altogether, these packages represent a fundamental step in the understanding of the emergent hydrodynamic descriptions of non-equilibrium quantum systems.