论文标题
绝对连续的量子树光谱
Absolutely Continuous Spectrum for Quantum Trees
论文作者
论文摘要
我们研究有限锥类型的量子树的光谱。这些是量子图，其几何形状具有一定的均匀性，并且在边缘上具有有限的边缘长度，耦合常数和电势。我们显示了频谱由纯粹的连续频谱和一组离散的特征值组成。之后，我们在边缘长度和耦合水平上研究此类树木的随机扰动，并证明了纯交流光谱的稳定性以及分析估计。
We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum, along with a discrete set of eigenvalues. Afterwards, we study random perturbations of such trees, at the level of edge length and coupling, and prove the stability of pure AC spectrum, along with resolvent estimates.
