arXiv ID: 2110.09339v1
Title: Finite sections of periodic Schrödinger operators
Language: English
Authors: Gabel, Fabian Nuraddin Alexander  
Gallaun, Dennis 
Großmann, Julian Peter  
Lindner, Marko  
Ukena, Riko 
Keywords: Mathematics - Spectral Theory; Mathematics - Spectral Theory; Computer Science - Numerical Analysis; Mathematical Physics; Mathematics - Mathematical Physics; Mathematics - Numerical Analysis; 65J10, 47B36 (Primary) 47N50 (Secondary)
Issue Date: 18-Oct-2021
Source: arXiv: 2110.09339v1 (2021)
Abstract (english): 
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.
Institute: Mathematik E-10 
Document Type: Preprint
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