标题： 非均匀阿贝尔Chern-Simons Higgs模型与新的非均匀BPS真空和孤立子 显示英文标题

标题： Inhomogeneous Abelian Chern-Simons Higgs Model with New Inhomogeneous BPS Vacuum and Solitons

摘要： 我们研究了一个具有磁性杂质的非均匀U(1) Chern-Simons Higgs模型，在BPS极限下。势能是六次方的，既有对称破缺相也有对称未破缺相，但其最小值随空间变化，取决于杂质的强度。虽然系统缺乏平移对称性，但它可以有一个超对称扩展。根据杂质项的符号，它要么有BPS部分，要么有反BPS部分（但不会同时存在），这些部分满足Bogomolny方程。对称破缺相的真空配置不再由势能的最小值简单确定，因为它不再是常数，而是满足Bogomolny方程的非平凡函数。因此，真空的能量和角动量密度在局部上具有非零分布，尽管总能量和角动量仍然为零。与均匀情况类似，该理论支持各种BPS孤子解，包括拓扑和非拓扑涡旋以及Q球。涡旋度以及U(1)电荷都是纯粹的正或负。对于高斯型杂质作为具体例子，我们得到了旋转对称的数值解并分析了它们的详细性质。我们还讨论了delta函数杂质的情况，即高斯杂质的无限薄极限，这显示出BPS Chern-Simons Higgs理论的一些非平凡特性。 显示英文摘要

摘要： We study an inhomogeneous U(1) Chern-Simons Higgs model with a magnetic impurity in the BPS limit. The potential is sextic with both broken and unbroken phases, but its minimum varies spatially depending on the strength of the impurity. While the system lacks translation symmetry, it admits a supersymmetric extension. Depending on the sign of the impurity term, it has either a BPS sector or an anti-BPS sector (but not both), which satisfies the Bogomolny equations. The vacuum configuration of the broken phase is not simply determined by the the minimum of the potential since it is no longer constant, but it becomes a nontrivial function satisfying the Bogomolny equations. Thus, the energy and angular momentum densities of the vacuum locally have nonzero distributions, although the total energy and angular momentum remain zero. As in the homogeneous case, the theory supports various BPS soliton solutions, including topological and nontopological vortices and Q-balls. The vorticities as well as the U(1) charges are exclusively positive or negative. For a Gaussian type impurity as a specific example, we obtain rotationally symmetric numerical solutions and analyze their detailed properties. We also discuss the case of a delta-function impurity as the infinitely thin limit of the Gaussian impurity which shows some nontrivial feature of BPS Chern-Simons Higgs theory.