Hydrodynamics and entropy production in low-dimensional quantum systems

In the past years, quantum non-equilibrium emerged as a new principal research arena, promising to assist the current development of new quantum technologies and to shine a new light on disparate fields of theoretical and experimental physics, from black holes to condensed matter and statistical physics. As quantum dynamics represents a major challenge for modern computational methods, relevant developments have come from devising new generalised and extended forms of classical hydrodynamic theory to effectively describe its macroscopic features. This effort is nowadays constituting an essential part of contemporary theoretical physics, contributing to a deeper understanding of dynamical phenomena and providing new directions in different experimental areas. This proposal focuses on the interplay between classical non-linear dynamics and quantum evolution, promising to a) unveil a new deep comprehension of how the non-equilibrium dynamics in many-body quantum systems can dissipate or either recover quantum information and how effective non-linear classical behaviour emerges, b) release new efficient theoretical tools to access quantum many-body quantum systems which are strongly interacting and in non-equilibrium settings beyond linear response, far away from known regimes of low-energy, low-temperatures or weak interactions. The outcomes will provide new reliable and much needed theoretical methods as well as a new dictionary to catalogue and relate different non-equilibrium phenomena in quantum and classical physics and deepen our understanding of out-of-equilibrium matter.