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)
Categories: cond-mat.other