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

TL;DR

This paper models the chaotic vortex lines in superfluid helium using Langevin dynamics, deriving a Gibbs distribution for vortex configurations and discussing implications for vortex statistics in counterflowing superfluid helium.

Contribution

It introduces a Langevin-force-based approach to vortex line dynamics in superfluid helium, deriving a Gibbs distribution for vortex configurations.

Findings

Derived a Fokker-Planck equation with a Gibbs distribution solution.

Connected vortex energy and Lamb impulse in the statistical description.

Discussed physical implications of the statistical model.

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)