Spectral Properties of Schr\"odinger Operators on Perturbed Lattices
Spectral Theory
2024-03-26 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We study the spectral properties of Schr\"{o}dinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorption principle for the resolvent, construct a spectral representation, and define the S-matrix. Our theory covers the square, triangular, diamond, Kagome lattices, as well as the ladder, the graphite and the subdivision of square lattice.
Keywords
Cite
@article{arxiv.1408.2076,
title = {Spectral Properties of Schr\"odinger Operators on Perturbed Lattices},
author = {Kazunori Ando and Hiroshi Isozaki and Hisashi Morioka},
journal= {arXiv preprint arXiv:1408.2076},
year = {2024}
}