离散结构上的哈密顿量：积分态密度的跳跃和一致收敛性
Hamiltonians on discrete structures: Jumps of the integrated density of states and uniform convergence
摘要：
研究了顺从几何上的等变离散哈密顿量族及其积分态密度。我们证明了固定能量的本征空间是由具有紧支集的本征函数张成的。因此，IDS的跳跃的大小由这样的本征函数所张成的子空间的等变维数给出。由此我们推出了一致收敛性（w.r.t.谱参数）的IDS的有限体积近似。我们的框架包括Delone集上的准周期算子，准传递图上的周期和随机算子，以及渗流图上的算子。
英文摘要：
We study equivariant families of discrete Hamiltonians on amenable geometries and their integrated density of states (IDS). We prove that the eigenspace of a fixed energy is spanned by eigenfunctions with compact support. The size of a jump of the IDS is consequently given by the equivariant dimension of the subspace spanned by such eigenfunctions. From this we deduce uniform convergence (w.r.t. the spectral parameter) of the finite volume approximants of the IDS. Our framework includes quasiperiodic operators on Delone sets, periodic and random operators on quasi-transitive graphs, and operators on percolation graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
