Perturbation of discriminant for one-dimensional discrete Schr\"odinger operator with sparse periodic potential
Mathematical Physics
2022-11-08 v1 math.MP
Abstract
We consider the one-dimensional discrete Schr\"odinger operator with complex-valued sparse periodic potential. The spectrum for a complex-valued periodic potential is a complicated compact set in the complex plane represented by real intersections of algebraic curves determined by a discriminant. We represent the discriminant by Chebyshev polynomials and use perturbations of the discriminant to study the spectrum.
Keywords
Cite
@article{arxiv.2211.03326,
title = {Perturbation of discriminant for one-dimensional discrete Schr\"odinger operator with sparse periodic potential},
author = {Masahiro Kaminaga},
journal= {arXiv preprint arXiv:2211.03326},
year = {2022}
}
Comments
17 pages, 3 figures