论文标题
周期图的分散关系中全球极值的本地测试
A local test for global extrema in the dispersion relation of a periodic graph
论文作者
论文摘要
我们考虑了一个周期性紧密结合模型（组合图）的家族，这些模型具有最小的基本域副本之间的链接。对于这个家庭，我们建立了第二个衍生物类型的局部状况，在该条件下，分散关系的临界点可以被认为是全球最大值或最小值。在时间反向对称性的额外假设下，我们表明，如果周期性组的维度为三个或更少，或者（在任何维度上），如果临界点是floquet--- floquet-- bloch家族的对称点，则实际上，分散带的任何局部极值实际上都是其全球极值。我们证明我们的结果几乎是最佳的，其中有许多示例。
We consider a family of periodic tight-binding models (combinatorial graphs) that have the minimal number of links between copies of the fundamental domain. For this family we establish a local condition of second derivative type under which the critical points of the dispersion relation can be recognized as global maxima or minima. Under the additional assumption of time-reversal symmetry, we show that any local extremum of a dispersion band is in fact its global extremum if the dimension of the periodicity group is three or less, or (in any dimension) if the critical point in question is a symmetry point of the Floquet--Bloch family with respect to complex conjugation. We demonstrate that our results are nearly optimal with a number of examples.
