论文标题
定期图的量子牙
Quantum ergodicity for periodic graphs
论文作者
论文摘要
我们证明了一个定期施罗丁·运营商的家族在定期图中$ h $ $ h $。这意味着，在大型有限周期图上，$ h $的大多数本征函数在某种意义上是等分分配的，因此将其定位。我们的结果涵盖了$ \ mathbb {z}^d $，三角形晶格，蜂窝晶格，笛卡尔产品和定期Schrödinger运营商的邻接矩阵。该定理更普遍地适用于任何满足Floquet特征值假设的周期性运算符。
We prove quantum ergodicity for a family of periodic Schrödinger operators $H$ on periodic graphs. This means that most eigenfunctions of $H$ on large finite periodic graphs are equidistributed in some sense, hence delocalized. Our results cover the adjacency matrix on $\mathbb{Z}^d$, the triangular lattice, the honeycomb lattice, Cartesian products and periodic Schrödinger operators on $\mathbb{Z}^d$. The theorem applies more generally to any periodic Schrödinger operator satisfying an assumption on the Floquet eigenvalues.
