算子谱和安德森局域化的关系

[forecasting]

看看算子谱和安德森局域化的关系。可以反过来看，根据势场粒子的行为反推相对应的算子的谱？有没有实验或观测？


Abstract：The article explores the interplay between natural boundaries in complex analysis and spectral theory, particularly in the context of Jacobi matrices and orthogonal polynomials. Here is a summary:
https://nms.kcl.ac.uk/alexander.pushnit ... /simon.pdf

Abstract：I explore some consequences of a groundbreaking result of Breimesser and Pearson on the absolutely continuous spectrum of one-dimensional Schr"odinger operators. These include an Oracle Theorem that predicts the potential and rather general results on the approach to certain limit potentials. In particular, we prove a Denisov-Rakhmanov type theorem for the general finite gap case.
The main theme is the following: It is extremely difficult to produce absolutely continuous spectrum in one space dimension and thus its existence has strong implications.

https://arxiv.org/abs/0706.1101