Finite sections of periodic Schrödinger operators

Publikationstyp
Preprint
Date Issued
2021-10-18
Sprache
English
Author(s)
Gabel, Fabian Nuraddin Alexander 
Gallaun, Dennis  orcid-logo
Großmann, Julian Peter  orcid-logo
Lindner, Marko  orcid-logo
Ukena, Riko  orcid-logo
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/10707
Citation
arXiv: 2110.09339 (2021)
Publisher DOI
10.48550/arXiv.2110.09339
ArXiv ID
2110.09339v1
We study discrete Schrödinger operators H with periodic potentials as they are typically used to approximate aperiodic Schrödinger operators like the Fibonacci Hamiltonian. We prove an efficient test for applicability of the finite section method, a procedure that approximates H by growing finite square submatrices Hn. For integer-valued potentials, we show that the finite section method is applicable as soon as H is invertible. This statement remains true for {0, λ}-valued potentials with fixed rational λ and period less than nine as well as for arbitrary real-valued potentials of period two.
Subjects
Mathematics - Spectral Theory
Mathematics - Spectral Theory
Computer Science - Numerical Analysis
Mathematical Physics
Mathematics - Mathematical Physics
Mathematics - Numerical Analysis
65J10, 47B36 (Primary) 47N50 (Secondary)
DDC Class
510: Mathematik