Verlagslink DOI: 10.48550/arXiv.2110.09339
arXiv ID: 2110.09339v1
Titel: Finite sections of periodic Schrödinger operators
Sprache: Englisch
Autor/Autorin: Gabel, Fabian Nuraddin Alexander  
Gallaun, Dennis 
Großmann, Julian Peter  
Lindner, Marko  
Ukena, Riko 
Schlagwörter: Mathematics - Spectral Theory; Mathematics - Spectral Theory; Computer Science - Numerical Analysis; Mathematical Physics; Mathematics - Mathematical Physics; Mathematics - Numerical Analysis; 65J10, 47B36 (Primary) 47N50 (Secondary)
Erscheinungs­datum: 18-Okt-2021
Quellenangabe: arXiv: 2110.09339v1 (2021)
Zusammenfassung (englisch): 
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.
URI: http://hdl.handle.net/11420/10707
Institut: Mathematik E-10 
Dokumenttyp: Vorabdruck (Preprint)
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