Linearized regime of the generalized hydrodynamics with diffusion

Understand

We consider the generalized hydrodynamics including the recently introduced diffusion term for an initially inhomogeneous state in the Lieb-Liniger model.

• We construct a general solution to the linearized hydrodynamics equation in terms of the eigenstates of the evolution operator and study two prototypical classes of initial states: delocalized and localized spatially.
• We exhibit some general features of the resulting dynamics, among them, we highlight the difference between the ballistic and diffusive evolution.
• The first one governs a spatial scrambling, the second, a scrambling of the quasi-particles content.