The Essential Spectrum of One-Dimensional Dirac Operators with Delta Interactions

2020 ◽  
Vol 54 (2) ◽  
pp. 145-148
Author(s):  
V. S. Rabinovich
Keyword(s):  
Essential Spectrum ◽  
Dirac Operators ◽  
One Dimensional

scholarly journals On spectral deformations and singular Weyl functions for one-dimensional Dirac operators

2015 ◽  
Vol 56 (1) ◽  
pp. 012102 ◽  
Author(s):  
Alexander Beigl ◽  
Jonathan Eckhardt ◽  
Aleksey Kostenko ◽  
Gerald Teschl
Keyword(s):  
Dirac Operators ◽  
One Dimensional ◽  
Weyl Functions

scholarly journals Singular Weyl–Titchmarsh–Kodaira theory for one-dimensional Dirac operators

2013 ◽  
Vol 174 (4) ◽  
pp. 515-547 ◽  
Author(s):  
Rainer Brunnhuber ◽  
Jonathan Eckhardt ◽  
Aleksey Kostenko ◽  
Gerald Teschl
Keyword(s):  
Dirac Operators ◽  
One Dimensional

scholarly journals Absolutely continuous spectrum of Dirac operators with square-integrable potentials

2014 ◽  
Vol 144 (3) ◽  
pp. 533-555
Author(s):  
Daniel Hughes ◽  
Karl Michael Schmidt
Keyword(s):  
Spectral Function ◽  
Continuous Spectrum ◽  
Scattering Problem ◽  
Dirac Operators ◽  
Mass Term ◽  
Absolutely Continuous Spectrum ◽  
Continuous Part ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
The One

We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (−∞, −1] ∪ [1, ∞). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a subsequent limiting procedure for the spectral function. Furthermore, we show that the absolutely continuous spectrum persists when an angular momentum term is added, thus also establishing the result for spherically symmetric Dirac operators in higher dimensions.

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