An investigation of application of sourcity in identification of a quantum vortex: identification of divergence characteristics of probability flow

The present study investigates the application of a geometrical quantity, sourcity, in the identification of a quantum vortex in a quantum turbulence. This quantity specifies the unidirectionality and intensity of the radial flow in a vector field in terms of the local flow geometry, which has been used to investigate the detail geometry of vortices in a classical turbulent flow. A quantum vortex is difficult to be identified with focusing on a swirling flow feature because the gradient tensor of superfluid has no rotational component except points of topological defect, i.e., quantum vortices. On the other hand, probability flow or the gradient vector of absolute value of a wave function has an outflow characteristic in a quantum vortex, which suggests that the application of the sourcity may contribute to the identification of this feature. A joint probability density function of the sourcity and magnitude of a wave function indicates a high correlation in a Direct Numerical Simulation of the Gross-Pitaevskii equation. The sourcity may be a candidate in the identification method of a quantum vortex.