Towards an ab initio derivation of generalised hydrodynamics from a gas of interacting wave packets

We present steps towards an ab initio derivation of generalised hydrodynamics in quantum integrable models, starting from the Bethe wave functions, and explained on the example of the repulsive Lieb-Liniger model. This includes an identification of the generalised hydrodynamics quasi-particles as wave packets in the quantum model. These wave packets evolve according to a classical particle model and collect two-particle scattering shifts similar to solitons in integrable PDEs. We then discuss potential routes to obtain the generalised hydrodynamics equation for average conserved densities in long-wavelength states from this description. As part of this, we provide an explicit formula for the action of the spectral phase-space density operator on Bethe wave functions, and show that it generates local conserved densities.