标题： 平坦能带的标量模型中的WKB结构 显示英文标题

标题： WKB structure in a scalar model of flat bands

摘要： 我们考虑一族周期性标量算子，根据Floquet--Bloch理论，可以定义平坦带。 一个源于近期物理文献的令人困惑的问题是这些平坦带出现时参数值的量化规则。 我们提出了关于相应方程解的结构的一般定理，并给出了一个启发式论证，解释了在特定情况下它们的WKB结构。 该结构也解释了量化条件——WKB结构和该规则都通过数值实验得到了验证。 最后，我们考虑了一个简化模型，在该模型中变量分离允许使用复数WKB方法。 显示英文摘要

摘要： We consider a family of periodic scalar operators for which one can define flat bands in the sense of Floquet--Bloch theory. One puzzling question originating in recent physics literature is a quantisation rule for the values of parameters at which these flat bands occur. We present a general theorem about the structure of solutions to the corresponding equation and a heuristic argument explaining their WKB structure in a specific case. That structure also explains the quantisation condition -- both the WKB structure and that rule are confirmed by numerical experiments. Finally, we consider a simplified model in which separation of variables allows the use of complex WKB methods.