Quantum Statistics of Three-Dimensional Vortex Filament in Superfluid 4He

The quantum statistics of three-dimensional vortex filament in superfluid⁴He is investigated by the use of path integral techniques. The free energy evaluated in the saddle point approximation decreases abruptly at a certain critical value of the applied superflow velocity. This critical behavior is in quantitative agreement with the experimental result of vortex nucleation by a moving ion. The dissipation effects are also discussed within the damped harmonic oscillator approximation.