QUantum Emergent Hydrodynamics of integrable many-body Systems : from Theory to applications and experimental validation (QuEHST)

Quantum physical systems consisting a large number of particles are difficult to study: this is well known in the context of statistical physics, whose "holy grail" is to understand the emergent behaviour of such systems starting from the microscopic models.

When many-body systems are probed at distances and time scales 'large enough' (at mesoscopic scales), their emergent and rather complex behaviour is well described by hydrodynamics. The latter can be described as the observation that the motion of many interacting particles is constrained by local conservation laws: the hydrodynamic equations, in fact, are basically continuity equations relating density and current density associated with the conserved quantities themselves.
While for generic systems with a few conserved quantities (tipically energy, momentum and number of particles), this is known since a long time, a similar hydrodynamic framework was only recently unveiled for systems possessing infinitely many of such conservation laws, i.e., integrable models (known for escaping standard thermalization to the Gibbs ensemble). This theory is known as Generalized Hydrodynamics (GHD).

But, how 'quantum' are the current hydrodynamic descriptions of quantum systems? In fact, the local relaxation assumption implies quantum decoherence among different fluid cells and, therefore, notably, the loss of equal-time long-range quantum correlations among the fluid cells (including zero entanglement).
From there, the necessity to re-quantize such theories, and in particular, of relevance for us, GHD. This is what we achieved in 2020, by establishing the theory of Quantum Generalized Hydrodynamics (QGHD).

This framework already proved able to give, in an elegant and simple fashion, non-trivial analytic predictions for quantities which were, before, thought inaccessible, especially in the case of fully interacting models. Still, it is relatively new, and therefore there are many open questions calling for an answer....