标题： 关于扰动环形涡旋能量量子化的群论方法：管道型区域中的谱计算 显示英文标题

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

摘要： 在本研究中，首次解决了量子涡旋环在细长管道中运动的能量谱问题。 我们使用一种新方法对该动力系统进行量子化，这导致了环绕值$\Gamma$和能量值$E$的非平凡结果。 结果显示，光谱具有准连续的分形结构。 最终形式中，我们将涡旋环的光谱表示为“Regge轨迹”$E = E(\Gamma)$。 该涡旋量子化问题是在两流体流体力学和其他传统方法之外考虑的。 我们还讨论了改进模型的方法，这可能使我们能够应用所获得的结果来描述量子湍流。 显示英文摘要

摘要： 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.