论文标题
双曲带理论中的Selberg Trace公式
Selberg trace formula in hyperbolic band theory
论文作者
论文摘要
我们将Selberg的痕量公式应用于双曲线理论中的问题，这是Bloch理论最近开发的扩展，以模拟实验实现双曲线晶格的模型带结构。为此，我们将高维晶体动量纳入痕量公式，并评估二属Bolza表面上的周期轨道的求和。我们应用该技术来计算在Bolza表面上的功能，并提出了Bolza表面上最低带和$ \ {8,3 \} $双曲晶格之间的近似关系。我们讨论了自动形态对称性及其在痕量公式中的表现的作用。
We apply Selberg's trace formula to solve problems in hyperbolic band theory, a recently developed extension of Bloch theory to model band structures on experimentally realized hyperbolic lattices. For this purpose we incorporate the higher-dimensional crystal momentum into the trace formula and evaluate the summation for periodic orbits on the Bolza surface of genus two. We apply the technique to compute partition functions on the Bolza surface and propose an approximate relation between the lowest bands on the Bolza surface and on the $\{8,3\}$ hyperbolic lattice. We discuss the role of automorphism symmetry and its manifestation in the trace formula.
