论文标题
liouville方程和准球面的涡流解决方案
Vortex solutions of Liouville equation and quasi spherical surfaces
论文作者
论文摘要
我们确定了与数学物理学重要性的某些解决方案相对应的二维表面，非本质的Chern-simons（或Jackiw-Pi）涡流解决方案，其特征在于整数$ n \ ge 1 $。这样的表面，我们称为$ s^2（n）$，具有正常的高斯曲率，$ k $，但仅在$ n = 1 $时才是球。它们具有边缘，对于任何固定的$ k $，都具有最大半径$ c $，我们在这里发现为$ c = n / \ sqrt {k} $。如果通过使用石墨烯（或任何其他狄拉克材料）在实验室中构建此类表面，我们的发现可能引起人们对非平凡背景上的桌面无质量激发的感兴趣。我们还简要讨论了作为产品$ s^2（n）\ times \ mathbb {r} $获得的三维空间的类型。
We identify the two-dimensional surfaces corresponding to certain solutions of the Liouville equation of importance for mathematical physics, the non-topological Chern-Simons (or Jackiw-Pi) vortex solutions, characterized by an integer $N \ge 1$. Such surfaces, that we call $S^2 (N)$, have positive constant Gaussian curvature, $K$, but are spheres only when $N=1$. They have edges, and, for any fixed $K$, have maximal radius $c$ that we find here to be $c = N / \sqrt{K} $. If such surfaces are constructed in a laboratory by using graphene (or any other Dirac material), our findings could be of interest to realize table-top Dirac massless excitations on nontrivial backgrounds. We also briefly discuss the type of three-dimensional spacetimes obtained as the product $S^2 (N) \times \mathbb{R}$.
