Turbulence in a Bose-Einstein condensate

We numerically model turbulence in a trapped atomic Bose–Einstein condensate by solving the Gross–Pitaevskii nonlinear Schroedinger equation. We find that, after an initial growth, the vortex length decays approximately as t−1 where t is time, consistent with experiments in turbulent superfluid helium, and that the velocity components obey power-law statistics, again in agreement with observations in turbulent superfluid helium. We find the same statistics, which contrasts to the Gaussian statistics observed in ordinary classical turbulence, in a variety of quantum fluids in two and three dimensions (trapped condensates, homogeneous condensates, vortex points, vortex filaments). We argue that the non-Gaussianity arises from the singular nature of quantised vorticity.