Anderson localization for block jacobi operators with quasi-periodic meromorphic potential

有限间隙Herglotz函数和周期Jacobi矩阵的亚纯延拓

Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices

本文给出了周期Jacobi矩阵指数衰减扰动的谱测度的Borel变换是Herglotz函数$m$的一个充要条件.该条件是根据$m$到自然黎曼曲面的亚纯延拓及其零点和极点的结构。对于拟周期Jacobi矩阵的谱测度的Borel变换也得到了类似的结果。本文推广了文[17]关于自由Jacobi矩阵指数衰减扰动的相应结果。

单频拟周期块Jacobi算子的安德森局域化

Anderson localization for one-frequency quasi-periodic block Jacobi operators

考虑一个单频拟周期块Jacobi算子，其块是一般矩阵值解析函数。在耦合常数足够大但与频率无关的假设下，我们建立了这类算子的安德森局域化。这推广了J. Bourgain和S. Jitomirskaya关于带格、准周期薛定谔算子的局部化。

Anderson Localization for Radial Tree Graphs With Random Branching Numbers

We prove Anderson localization for the discrete Laplace operator on radial tree graphs with random branching numbers. Our method relies on the representation of the Laplace operator as the direct sum of half-line Jacobi matrices whose entries are non-degenerate, independent, identically distributed random variables with singular distributions.

树上周期Jacobi矩阵的一个有用公式

A Useful Formula for Periodic Jacobi Matrices on Trees

本文针对树上周期Jacobi矩阵引入态密度函数并证明其有用公式，简化了能隙标记和Aomoto指标定理的证明，并推广至Anderson模型。

Spectral Theory of one-channel operators and application to absolutely continuous spectrum for Anderson type models

A one-channel operator is a self-adjoint operator on $\ell^2(\mathbb{G})$ for some countable set $\mathbb{G}$ with a rank 1 transition structure along the sets of a quasi-spherical partition of $\mathbb{G}$. Jacobi operators are a very special case. In essence, there is only one channel through which waves can travel across the shells to infinity. This channel can be described with transfer matrices which include scattering terms within the shells and connections to neighboring shells. Not all of the transfer matrices are defined for some countable set of energies. Still, many theorems from th…

准周期 Jacobi 块矩阵的非微扰局域化

Non-perturbative localization for quasi-periodic Jacobi block matrices

本文证明了在所有 Lyapunov 指数非零且基础动力学为 Diophantine 旋转的假设下，准周期 Jacobi 块矩阵算子的非微扰 Anderson 局域化，并探讨了其在 $b=1$ 时的算术局域化及相关物理模型中的应用。