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

• URL: http://arxiv.org/abs/2403.06441v3
• Date: Fri, 22 Nov 2024 06:44:25 GMT
• Title: On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain
• Authors: S. V. Talalov,
• Abstract summary: We present the problem of the energy spectrum of a quantum vortex loop moving in a thin long pipe. We quantize this dynamic system using a new method, which leads to non-trivial results for circulation. We 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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• 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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