A universal holographic prediction for quantum-critical dynamics

We consider decay of an initial density or current perturbation at finite temperature $T$ near a quantum critical point with emergent Lorentz invariance. We argue that decay of perturbations with wavenumbers $k \gg T$ (in natural units) is a good testing ground for holography---existence of a dual gravitational description---in experimentally accessible systems. The reason is that, computed holographically, the decay rate at large $k$ depends only on the leading correction to the metric near the boundary, and that is quite universal. In the limit of zero detuning (when the temperature is the only dimensionful parameter), the result is a scaling law for the decay rate, with the exponent that depends only on the dimensionality. We show that this follows from an analytical argument and is borne out by a numerical study of quasinormal modes.