Path Integral Approach to Vortex Filament in Superfluid ⁴He

Abstract

The quantum statistics of a three-dimensional vortex filament under an applied superflow in superfluid ⁴He is investigated by the use of path integral techniques. The free energy evaluated in the saddle point approximation around a static vortex decreases abruptly at a certain critical value of the applied superflow velocity. This critical behavior is consistent with the experimental result of vortex nucleation by a moving ion. The dissipation effects are also discussed within the context of the damped harmonic oscillator approximation.