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arXiv 0908.2621hep-thhep-ph
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扭弦的不稳定性

Instabilities of Twisted Strings

Peter Forgacs, Arpad Lukacs

摘要:

本文用SU(2)半局域理论--具有两个整体SU(2)对称的带电标量场的阿贝尔-希格斯模型--对扭曲磁通管(弦)进行了线性稳定性分析。这里的扭曲是指两个复数标量之间的相对相位(与$z$坐标呈线性相关),重要的是它导致了一个全局电流沿着弦流动。这样的扭弦分叉的Abrikosov-Nielsen-Olesen(ANO)的解决方案嵌入在半局部理论。我们的小波动谱的数值研究证实了以前的结果,扭曲的字符串表现出不稳定性,其振幅随时间呈指数增长。更准确地说,具有单个磁通量量子的扭弦允许具有谐波$z$依赖性的不稳定本征模的连续族,其由波数$k\in[-k_{\rm m},k_{\rm m}]$索引。进行摄动半解析分析的分歧,它被发现,纯数值结果是非常好地再现。这样,人们不仅得到了扭曲的解决方案本身以及它们的不稳定性的一个很好的定性描述,但也是一个定量描述的数值结果。我们的半解析结果表明,在密切类似于已知的嵌入ANO涡的不稳定性,扭绳也可能扩大的大小所造成的扩散出的磁通量。

英文摘要:

A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory -- an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry -- is carried out. Here the twist refers to a relative phase between the two complex scalars (with linear dependence on, say, the $z$ coordinate), and importantly it leads to a global current flowing along the the string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO) solution embedded in the semilocal theory. Our numerical investigations of the small fluctuation spectrum confirm previous results that twisted strings exhibit instabilities whose amplitudes grow exponentially in time. More precisely twisted strings with a single magnetic flux quantum admit a continuous family of unstable eigenmodes with harmonic $z$ dependence, indexed by a wavenumber $k\in[-k_{\rm m},k_{\rm m}]$. Carrying out a perturbative semi-analytic analysis of the bifurcation, it is found that the purely numerical results are very well reproduced. This way one obtains not only a good qualitative description of the twisted solutions themselves as well as of their instabilities, but also a quantitative description of the numerical results. Our semi-analytic results indicate that in close analogy to the known instability of the embedded ANO vortex a twisted string is also likely to expand in size caused by the spreading out of its magnetic flux.

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