Perturbation of discriminant for one-dimensional discrete Schrödinger operator with sparse periodic potential

2022/11/07 by Masahiro Kaminaga, Kaminaga, Masahiro
Computer Science · Mathematics · #47A10 #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2211.03326

openalex publication_date 2022/11/07 · openalex created_date 2022/11/13 · openalex updated_date 2026/07/28

Abstract

We consider the one-dimensional discrete Schrödinger 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.

Related

• On a Question of Poltoratski
• Floquet Isospectrality of the Zero Potential for Discrete Periodic Schrödinger Operators
• On the spectrum of discrete Schrödinger equation with one-dimensional perturbation
• Universal algorithms for computing spectra of periodic operators
• Fourier method for one dimensional Schrödinger operators with singular periodic potentials