Avalanche statistics and intermittency in topological defect-mediated flows

Topological defects dominate the deformation response of materials in processes ranging from quantum turbulence to crystal plasticity. We calculate the probability distribution function for the fluctuations in velocity $v$, using scaling arguments and a systematic cluster expansion method to account for density correlations. We find that the distribution has power-law tails with an exponent that takes the value -3 for $v\to \mathrm{\infty }$, but a value -2 for intermediate values of $v$. We relate these regimes to the theory of avalanches, by directly computing the known avalanche scaling exponents.