论文标题
漏洞标记为泡泡二叉戟自相似图的定理
Gaps labeling theorem for the Bubble-diamond self-similar graphs
论文作者
论文摘要
Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians使用光谱拆卸技术。通过标准化的特征值计数函数（也称为状态的集成密度）将槽中的差距标记，我们将间隙标签描述为第二个动态系统的轨道，该轨道反映了气泡结构的分支参数和拆卸结构。极限图上的天然拉普拉斯元素的光谱通常显示为在cantor集合上支撑的纯点，尽管一个特定的图具有纯点和奇异连续的组件的混合物。
Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.
