Wigner's distribution and the quantized vortex

A quantum model for the vorticity of a single fluctuating rectilinear vortex is obtained by assuming Wigner's distribution for the vorticity. The starting point for this calculation is Fetter's quantum theory of the superfluid vortex, in which the vortex waves are induced by a quantum rather than a classical random noise source. Thermal averaging of the quantum model does, however, give the classical result for the distribution. From the vorticity, a quantum model for the velocity around the vortex is obtained. A thermal averaging of the velocity allows an explicit verification of McCauley's proposal that the effect of quantum fluctuations is to smear out the vortex singularity and give the appearance of a classical core. A quantum model for the kinetic energy density is also obtained. From this it is found that the zero-point velocities are uncorrelated.