On the universality of AdS$_2$ diffusion bounds and the breakdown of linearized hydrodynamics

The chase of universal bounds on diffusivities in strongly coupled systems and holographic models has a long track record. The identification of a universal velocity scale, independent of the presence of well-defined quasiparticle excitations, is one of the major challenges of this program. A recent analysis, valid for emergent IR fixed points exhibiting local quantum criticality, and dual to IR AdS$_2$ geometries, suggests to identify such a velocity using the time and length scales at which hydrodynamics breaks down -- the equilibration velocity. The latter relates to the radius of convergence of the hydrodynamic expansion and it is extracted from a collision between a hydrodynamic diffusive mode and a non-hydrodynamic mode associated to the IR AdS$_2$ region. In this short note, we confirm this picture for holographic systems displaying the spontaneous breaking of translational invariance. Moreover, we find that, at zero temperature, the lower bound set by quantum chaos and the upper one defined by causality and hydrodynamics exactly coincide, determining uniquely the diffusion constant. Finally, we comment on the meaning and universality of this newly proposed prescription.