Report on scipost_202005_00007v1

Abstract

We study the presence of universal bounds on transport in homogeneous holographic models with broken translations. We prove numerically that, in holographic systems with momentum dissipation, the viscosity to entropy bound might be violated but the shear diffusion constant remains bounded by below. This confirms the idea that η/s is not a meaningful quantity in non-relativistic systems and that, in order to find more universal bounds, one should rather look at diffusion constants. We strengthen this idea by showing that, in presence of spontaneously broken translations, the Goldstone diffusion constant satisfies a universal lower bound in terms of the Planckian relaxation time and the butterfly velocity. Additionally, all the diffusive processes in the model satisfy an upper bound, imposed by causality, which is given in terms of the thermalization time-the imaginary part of the first non-hydrodynamic mode in the spectrum-and the speed of longitudinal sound. Finally, we discuss the existence of a bound on the speed of sound in holographic conformal solids and we show that the conformal value acts as a lower (and not upper) bound on the speed of longitudinal phonons. Nevertheless, we prove that the stiffness ∂p/∂ is still bounded by above by its conformal value. This suggests that the bounds conjectured in the past have to be considered on the stiffness of the system, related to its equation of state, and not on the propagation speed of sound. Contents 4.2 Results from holography 16 5 Bounds on the speed of sound and the stiffness 17 6 Conclusions 21 References 23