Langevin dynamics of vortex lines in the counterflowing He II. Talk given at the Low Temperature Conference, Kazan, 2015

Abstract: The problem of the statistics of a set of chaotic vortex lines in a counterflowing superfluid helium is studied. We introduced a Langevin-type force into the equation of motion of the vortex line in presence of relative velocity $\mathbf{v_{ns}}$. This random force is supposed to be Gaussian satisfying the fluctuation-dissipation theorem. The corresponding Fokker-Planck equation for probability functional in the vortex loop configuration space is shown to have a solution in the form of Gibbs distribution with the substitution $E{\mathbf{s}\rightarrow }E({\mathbf{% s}-P(v_{n}-v_{s})}$, where $E{\mathbf{s}}$ is the energy of the vortex configuration ${\mathbf{s}}$, and $\mathbf{P}$ is the Lamb impulse. Some physical consequences of this fact are discussed.\ \newline PACS numbers: 47.32.C- (Vortex dynamics) 47.32.cf (Vortex reconnection and rings), 47.37.+q (Hydrodynamic aspects of superfluidity)