The quantum vortices dynamics: spatio-temporal scale hierarchy and origin of turbulence

Abstract: This study investigates the evolution and interaction of quantum vortex loops with a small but non-zero radius of core ${\sf a}$. The quantization scheme of the classical vortex system is based on the approach proposed by the author \cite{Tal,Tal_PhRF}. We consider small perturbations in the ring-shaped loops, which include both helical-type shape variations and small excitations of the flow in the vortex core. The quantization of the circulation $\Gamma$ is deduced from the first principles of quantum theory. As a result of our approach, the set of quantized circulation values is wider than the standard one. The developed theory introduces a hierarchical spatio-temporal scale in the quantum evolution of vortices. We also explore the applicability of this model for describing the origins of turbulence in quantum fluid flows. To achieve this specific objective, we employ the method of random Hamiltonians to describe the interaction of quantum vortex loops.