Holographic Vortex Liquids and Superfluid Turbulence

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Science  26 Jul 2013:
Vol. 341, Issue 6144, pp. 368-372
DOI: 10.1126/science.1233529

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Holographic Turbulence

Turbulence in a superfluid presents an even more challenging theoretical problem than classical turbulence. Chesler et al. (p. 368) studied simulated superfluid turbulence using holographic duality. The direction of the energy flow in a two-dimensional superfluid was opposite to that in classical fluids—the energy injected at long length scales dissipated at short length scales through the vortices that form in a turbulent superfluid.


Superfluid turbulence is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic approach to studying such quantum turbulence by mapping the dynamics of a strongly interacting quantum liquid into the dynamics of classical gravity. We use this gravitational description to numerically construct turbulent flows in a holographic superfluid in two spatial dimensions. We find that the superfluid kinetic energy spectrum obeys the Kolmogorov Embedded Image scaling law, with energy injected at long wavelengths undergoing a direct cascade to short wavelengths where dissipation by vortex annihilation and vortex drag becomes efficient. This dissipation has a simple gravitational interpretation as energy flux across a black hole event horizon.

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