论文标题
在存在磁性杂质的情况下,$ dual $ cp(2)$类似涡流的孤子
Self-dual $CP(2)$ vortex-like solitons in the presence of magnetic impurities
论文作者
论文摘要
我们研究了通过包含磁性杂质扩展的两个测量值(2)$模型中涡流配置的存在。特别是,我们分别考虑了Maxwell-$ cp(2)$和Chern-Simons-$ cp(2)$放大的方案。我们选择$ CP(2)$ - 字段配置,不仅在最简单(免费)情况下,而且还选择了无效的拓扑费,而且还可以在耦合到Abelian Gauge字段时。 Bogomol'nyi-prasad-Sommerfield(BPS)形式主义的实现表明,这种配置的有效模型具有自偶有的结构,看起来像是测量的Sigma模型所固有的。因此,当$ cp(2)$场与麦克斯韦项耦合时,相应的总能量既具有定义明确的bogomol'nyi结合,又具有量化的磁通量。此外,当$ cp(2)$方案通过Chern-Simons动作量化时,总电荷被验证为与量化的磁通量成正比。此外,分析验证了磁杂质是否有助于BPS电位,并出现在两个模型的BPS方程中。接下来,我们引入高斯类型的杂质,并通过有限差异方案解决自偶联方程。所得的解决方案提出了一种非单调行为,可以翻转磁场和电场。最后,我们在杂质变为dirac $δ$功能的极限上讨论了拓扑琐碎的解决方案。
We investigate the existence of vortex configurations in two gauged-$CP(2)$ models extended via the inclusion of magnetic impurities. In particular, we consider both the Maxwell-$CP(2)$ and the Chern-Simons-$CP(2)$ enlarged scenarios, separately. We choose a $CP(2)$-field configuration with a null topological charge not only in the simplest (free) case, but also when coupled to an Abelian gauge field. The implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism shows that the effective models for such a configuration possess a self-dual structure which looks like those inherent to the gauged sigma models. Therefore, when the $CP(2)$ field is coupled to the Maxwell term, the corresponding total energy possesses both a well-defined Bogomol'nyi bound and a quantized magnetic flux. Further, when the $CP(2)$ scenario is gauged with the Chern-Simons action, the total electric charge is verified to be proportional to the quantized magnetic flux. In addition, the analysis verifies that the magnetic impurity contributes to the BPS potentials and appears in both the models' BPS equations. Next, we introduce a Gaussian type impurity and solve the self-dual equations via a finite-difference scheme. The resulting solutions present a nonmonotonic behavior that flips both the magnetic and electric fields. Finally, we discuss the topologically trivial solutions in the limit for which the impurity becomes a Dirac $δ$-function.