Absolutely continuous spectrum and ballistic transport in a one-dimensional quasiperiodic system

2013 ◽  
Author(s):  
Biplab Pal ◽  
Arunava Chakrabarti
Keyword(s):  
Continuous Spectrum ◽  
Ballistic Transport ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
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.

NOTE TO THE PAPER BY P. D. HISLOP AND S. NAKAMURA: STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS

1993 ◽  
Vol 05 (02) ◽  
pp. 453-456 ◽  
Author(s):  
GÜNTER STOLZ
Keyword(s):  
Continuous Spectrum ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Absolutely Continuous Spectrum ◽  
Random Potentials ◽  
Absolutely Continuous ◽  
One Dimensional

A physically non-satisfactory assumption in a result of Hislop and Nakamura [3] on the absence of absolutely continuous spectrum for one-dimensional Schrödinger operators is shown to be removable.

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