A universal holographic prediction for quantum-critical dynamics

Abstract

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.

5 pages, 2 figures; minor changes; references added

References in corpus (8)

• Quantum critical transport, duality, and M-theory
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Quasinormal modes of plane-symmetric black holes according to the AdS/CFT correspondence
• Quasinormal modes of black holes in anti-de Sitter space: a numerical study of the eikonal limit
• Damping of hard excitations in strongly coupled $\mathcal{N}=4$ plasma
• Shock waves in strongly coupled plasmas
• Bulk black hole, escaping photons, and bounds on violations of Lorentz invariance