Dense point spectrum and absolutely continuous spectrum in spherically symmetric Dirac operators

1995 ◽  
Vol 7 (7) ◽  
Author(s):  
Karl Michael Schmidt
Keyword(s):  
Continuous Spectrum ◽  
Point Spectrum ◽  
Dirac Operators ◽  
Spherically Symmetric ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
Dense Point

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.

scholarly journals Substitution-based structures with absolutely continuous spectrum

2018 ◽  
Vol 29 (4) ◽  
pp. 1072-1086 ◽  
Author(s):  
Lax Chan ◽  
Uwe Grimm ◽  
Ian Short
Keyword(s):  
Continuous Spectrum ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous
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