论文标题
圆锥上的$ P $液晶中的分数缺陷电荷
Fractional defect charges in $p$-atic liquid crystals on cones
论文作者
论文摘要
圆锥形表面具有高斯曲率在顶端的三角洲功能，也许是几何挫败感的最简单例子。我们在锥体表面上研究了具有$ p $折的旋转对称性（$ p $ atics）的二维液晶。在基部的自由边界条件下，我们发现基稳态状态的基态和离散的梯子是锥角和液晶对称性$ p $的函数。我们发现这些状态的特征是顶端的一组分数缺陷电荷，并且由于平行运输沿锥的方向方向的影响，地面状态通常会沮丧。我们在数值上检查了基态能量的预测，以了解一组相称的锥角度（对应于集中在圆锥形顶点的一组相称的高斯曲线），它们的表面可以作为完美的三角形或方形的网格，并与我们的理论预测找到出色的一致性。
Conical surfaces, with a delta function of Gaussian curvature at the apex, are perhaps the simplest example of geometric frustration. We study two-dimensional liquid crystals with $p$-fold rotational symmetry ($p$-atics) on the surfaces of cones. For free boundary conditions at the base, we find both the ground state(s) and a discrete ladder of metastable states as a function of both the cone angle and the liquid crystal symmetry $p$. We find that these states are characterized by a set of fractional defect charges at the apex and that the ground states are in general frustrated due to effects of parallel transport along the azimuthal direction of the cone. We check our predictions for the ground state energies numerically for a set of commensurate cone angles (corresponding to a set of commensurate Gaussian curvatures concentrated at the cone apex), whose surfaces can be polygonized as a perfect triangular or square mesh, and find excellent agreement with our theoretical predictions.
