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

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  • Talalov, S.V.

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 Γ 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(Γ). 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 have obtained to describe a quantum turbulent flow.

Suggested Citation

  • Talalov, S.V., 2025. "On the group-theoretical approach to energy quantization of a perturbed vortex ring: Spectrum calculating in the pipe-type domain," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014759
    DOI: 10.1016/j.chaos.2024.115923
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