论文标题
用于散射量子图的散射共振的痕量公式
A trace formula for scattering resonances of unbalanced quantum graphs
论文作者
论文摘要
给定一个不平衡的开放量子图，我们得出了一个公式，将其在其散射谐振的谐振上与带外的积分相关。我们在共振的数量（在复杂平面的有界区域）上推断出独立于图的大小的下限。我们还推断出部分结果，表明开放量子图的Benjamini-Schramm收敛应意味着经验光谱测量的收敛性。
Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals outside a strip. We deduce lower bounds on the number of resonances (in bounded regions of the complex plane),that are independent of the size of the graph. We also deduce partial results indicating that Benjamini-Schramm convergence of open quantum graphs should imply convergence of the empirical spectral measures.
