On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909437152722944 |
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| author | Talalov, S. V. |
| author_facet | Talalov, S. V. |
| contents | 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've obtained to describe a quantum turbulent flow. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_06441 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain Talalov, S. V. Mathematical Physics Quantum Physics 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've obtained to describe a quantum turbulent flow. |
| title | On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2403.06441 |