超导半局域扭线的稳定性分析
Stability Analysis of The Twisted Superconducting Semilocal Strings
摘要：
研究了具有整体$\mathbf{SU}(2)$不变性的半局域阿贝尔Higgs模型中扭曲涡旋解的稳定性。这个模型可以看作是非阿贝尔规范场纠缠极限下的Weinberg-Salam理论，也可以看作是两分量的Ginzburg-Landau理论。扭转涡的特征是一个恒定的全球电流${\cal I}$，并为${\cal I}\to 0$，他们减少到半局域弦，即Abrikosov-Nielsen-Olesen涡嵌入到半局域模型。具有${\cal I}\neq 0$的解更复杂，特别是，它们比半局部弦{ \it能量更低}，这使得人们希望它们可以具有更好的稳定性。我们考虑了线性微扰理论中扭曲涡旋周围的一般场涨落，并应用Jacobi准则检验了涨落算符谱中负模的存在性。我们发现扭曲涡不具有半局域弦的均匀不稳定性，也不具有波长小于某个临界值的非均匀不稳定性。这意味着足够短的涡片是扰动稳定的，并表明小涡环可能也是稳定的。对于较长波长的扰动，在光谱中正好有一个负模式，其增长需要将均匀涡旋分割成不均匀的“香肠状”结构。这种不稳定性在性质上类似于水射流的流体动力学高原-瑞利不稳定性，或者类似于高维引力理论中黑弦的格雷戈里-拉弗拉姆不稳定性。
英文摘要：
We study the stability properties of the twisted vortex solutions in the semilocal Abelian Higgs model with a global $\mathbf{SU}(2)$ invariance. This model can be viewed as the Weinberg-Salam theory in the limit where the non-Abelian gauge field decouples, or as a two component Ginzburg-Landau theory. The twisted vortices are characterized by a constant global current ${\cal I}$, and for ${\cal I}\to 0$ they reduce to the semilocal strings, that is to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model. Solutions with ${\cal I}\neq 0$ are more complex and, in particular, they are {\it less energetic} than the semilocal strings, which makes one hope that they could have better stability properties. We consider the generic field fluctuations around the twisted vortex within the linear perturbation theory and apply the Jacobi criterion to test the existence of the negative modes in the spectrum of the fluctuation operator. We find that twisted vortices do not have the homogeneous instability known for the semilocal strings, neither do they have inhomogeneous instabilities whose wavelength is less than a certain critical value. This implies that short enough vortex pieces are perturbatively stable and suggests that small vortex loops could perhaps be stable as well. For longer wavelength perturbations there is exactly one negative mode in the spectrum whose growth entails a segmentation of the uniform vortex into a non-uniform, `sausage like' structure. This instability is qualitatively similar to the hydrodynamical Plateau-Rayleigh instability of a water jet or to the Gregory-Laflamme instability of black strings in the theory of gravity in higher dimensions.
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