AI 中文总结
本研究提出含杂质的涡旋模型，通过坐标变换映射BPS方程，识别镜像非局域杂质产生对称涡旋-反涡旋对，推导模空间度量并扩展至多涡旋阵列，还引入径向凸包杂质生成特殊涡旋。
AI 中文摘要
在本研究中，我们提出了一种涡旋-杂质模型，该模型允许包含涡旋和反涡旋的BPS构型，且可在模空间近似框架内描述涡旋-反涡旋湮灭过程。对于一类合适的杂质，通过坐标变换可将BPS方程映射至无杂质的Abelian-Higgs模型的BPS方程。我们特别识别出作为镜像的非局域杂质，其会产生相对于杂质对称放置的涡旋-反涡旋对。我们推导了对应的模空间度量，并证明在测地线近似下，该对会渐近趋近于湮灭构型。我们进一步将该构造扩展至交替涡旋与反涡旋的链和二维阵列。最后，我们引入径向凸包杂质，其会产生具有非平凡内部磁结构的拉伸和压缩涡旋。
英文摘要
In this work, we introduce a vortex-impurity model that admits BPS configurations containing both vortices and antivortices and allows vortex-antivortex annihilation to be described within the moduli-space approximation. For a suitable class of impurities, the BPS equations can be mapped through a coordinate transformation onto those of the impurity-free Abelian-Higgs model. In particular, we identify nonlocalized impurities that act as mirrors, generating a vortex-antivortex pair symmetrically placed with respect to the impurity. We derive the corresponding moduli-space metric and show that, within the geodesic approximation, the pair approaches the annihilation configuration asymptotically. We further extend the construction to chains and two-dimensional arrays of alternating vortices and antivortices. Finally, we introduce radial bump impurities that produce stretched and compressed vortices with nontrivial internal magnetic structures.
