QUANTUM STATISTICS OF 3-DIMENSIONAL VORTEX FILAMENT IN SUPERFLUID HE-4

The quantum statistics of three-dimensional vortex filament in superfl uid He-4 is investigated by the use of path integral techniques. The f i ee energy evaluated in the saddle point approximation decreases abru ptly at a certain critical value of the applied superflow velocity. Th is critical behavior is in quantitative agreement with the experimenta l result of vortex nucleation by a moving ion. The dissipation effects are also discussed within the damped harmonic oscillator approximatio n. PACS numbers: 67.40.Db, 67.40.Vs.