论文标题
周期性图运算符的Bloch品种和量子
Bloch varieties and quantum ergodicity for periodic graph operators
论文作者
论文摘要
对于周期性的图形运算符，我们建立标准以确定基于Bloch品种的光谱带函数的重叠。一个标准指出，对于一个周期性的图形运算符，Bloch品种的不可约性意味着光谱带函数的非平凡时期。这尤其表明，离散周期性schrödinger运算符的光谱频带功能在$ \ mathbb {z}^d $上没有非平凡的时期，回答了McKenzie和Sabri提出的问题[定期图的量子符号。 ARXIV预印型ARXIV：2208.12685（2022）]。
For periodic graph operators, we establish criteria to determine the overlaps of spectral band functions based on Bloch varieties. One criterion states that for a large family of periodic graph operators, the irreducibility of Bloch varieties implies no non-trivial periods for spectral band functions. This particularly shows that spectral band functions of discrete periodic Schrödinger operators on $\mathbb{Z}^d$ have no non-trivial periods, answering a question asked by Mckenzie and Sabri [Quantum ergodicity for periodic graphs. arXiv preprint arXiv:2208.12685 (2022)].
