Statistics of Lagrangian quantum turbulence

We consider the dynamics of small tracer particles in turbulent quantum liquids. The complicated interaction processes of vortex filaments, the quantum constraints on vorticity and the varying influence of both the superfluid and the normal fluid on the tracer particle effectively lead to a superstatistical Langevin-like model that in a certain approximation can be solved analytically. An analytic expression for the PDF of velocity v of the tracer particle is derived that exhibits not only the experimentally observed $v^-3$ tails but also the correct behavior near the center of the distribution, in excellent agreement with experimental measurements and numerical simulations. Our results are universal and do not depend on details of the quantum fluid.

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