论文标题
周期性量子图中的退化带边缘
Degenerate band edges in periodic quantum graphs
论文作者
论文摘要
周期性结构连续光谱的带边缘是其浮雕的浮雕关系的最大值和最小值 - bloch转换。通常假定产生带边的极端是非分类的。 本文构建了$ \ mathbb {z}^3 $ - 周期性量子图的一系列示例，其中非分类假设失败了：沿着共同数字2的代数曲线可实现第一频段的最大值。示例示例对示例的代数曲线。对于边缘长度，vertex条件和边缘电势的范围，该示例是可靠的。构造背后的简单想法使概括得出了更复杂的图形和晶格尺寸。实现极值的曲线具有自然解释为平面多边形的模量空间。
Edges of bands of continuous spectrum of periodic structures arise as maxima and minima of the dispersion relation of their Floquet--Bloch transform. It is often assumed that the extrema generating the band edges are non-degenerate. This paper constructs a family of examples of $\mathbb{Z}^3$-periodic quantum graphs where the non-degeneracy assumption fails: the maximum of the first band is achieved along an algebraic curve of co-dimension 2. The example is robust with respect to perturbations of edge lengths, vertex conditions and edge potentials. The simple idea behind the construction allows generalizations to more complicated graphs and lattice dimensions. The curves along which extrema are achieved have a natural interpretation as moduli spaces of planar polygons.
