论文标题
圆柱域中的封闭涡流丝：循环量化
Closed Vortex Filament in a Cylindrical Domain: Circulation Quantization
论文作者
论文摘要
本文调查了零厚度为零的涡旋环的量子振荡，该环在圆柱域中演变为$ v = d \ times [0，l] $。符号$ d $表示由某些封闭的连接曲线$ s $界定的平面域。该动力系统的量化方案基于作者早期提出的方法。结果，我们发现流通$γ$的离散值$γ_n$。 与通常假定这种数量的传统方法相反，$γ_n$的值是按照量子理论的常规方案的结果进行严格推导的。该模型也证明了水平的分裂。特别是，级别校正值取决于域$ v $：气缸高$ l $和曲线$ s $的形式影响数量$γ_n$的最终公式。此外，我们证明了基本的循环水平表现出“精细的结构”。这些异常术语与$ \ hbar^2 $成正比的术语也在文章中计算出来。 将结论与其他作者的数值模拟结果进行了比较。
This article investigates quantum oscillations of a vortex ring with zero thickness that evolves in a cylindrical domain $V = D \times [0,L]$. The symbol $D$ denotes the planar domain which is bounded by some closed connected curve $S$. The quantization scheme of this dynamical system is based on the approach proposed by the author earlier. As result, we find the discrete values $Γ_n$ for circulation $Γ$. In contrast to the traditional approach, where such quantities are usually postulated, the values $Γ_n$ are deduced rigorously as the consequence of the conventional scheme of quantum theory. The model demonstrates the splitting of levels also. In particular, the levels correction values depend on the domain $V$: both the cylinder height $L$ and the form of the curve $S$ affect the final formula for the quantities $Γ_n$. Moreover, we prove that the basic circulation levels demonstrate a "fine structure". These anomalous terms, which are proportional to the value $\hbar^2$, are calculated in the article as well. The conclusions are compared with some results of numerical simulations by other authors.
