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arXiv · 2403.06441

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

S. V. Talalov
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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.

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S. V. Talalov. 2024-03-11. On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain. https://doi.org/10.1016/j.chaos.2024.115923

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