On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain

Abstract

In this study, the problem of the energy spectrum of a quantum vortex loop moving in a thin long pipe is solved for the first time. We quantize this dynamic system using a new method, which leads to non-trivial results for circulation $\Gamma$ and energy values $E$. It is shown that the spectrum has a quasi-continuous fractal structure. In the final form, we present the spectrum of the vortex loop in the form of a ''Regge trajectory'' $E=E(\Gamma )$. The vortex quantization problem is considered outside of two-fluid hydrodynamics and other conventional approaches. We also discuss ways to improve the model, which could allow us to apply the results we've obtained to describe a quantum turbulent flow.

13 pages, 1 figure

References in corpus (4)

• Small Oscillations of a Vortex Ring: Hamiltonian Formalism and Quantization
• Closed Vortex Filament in a Cylindrical Domain: Circulation Quantization
• Towards quantum turbulence theory: A simple model with interaction of the vortex loops
• The system of the vortex-like structures: the viewpoint on a turbulence modelling