On the universality of AdS2 diffusion bounds and the breakdown of linearized hydrodynamics

Abstract

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 AdS2 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 AdS2 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.

Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field

“…Thus our work shows that, in addition to the EXB case (energy diffusion bound), the pole-skipping also can capture the diffusion bound (crystal diffusion bound) for the SSB case in (3.29). 16 16 Our work also supports the hypothesis given in [74]: D ≥…”

Collective modes of polarizable holographic media in magnetic fields

“…This collision, and in particular the momentum k * 2 at which it happens, determines the radius of convergence of the linearized hydrodynamic expansion in this sector. More precisely, as shown in [49][50][51] and studied further in [52][53][54][55][56], the radius of convergence in momentum space, R, is given by…”

Quasinormal modes of a semi-holographic black brane and thermalization

“…We find that the diffusion constant D decreases monotonically with β and changes sign at βc ≈ 0. which ω D collides with ω Q ), and k * can be arbitrarily close to the origin for small β, it is very difficult to determine D at small values of β numerically. It has been argued that the diffusion constant should satisfy an upper bound [17][18][19][47][48][49] in a wide class of many-body systems, i.e.…”