One-dimensional Discrete Dirac Operators in a Decaying Random Potential I: Spectrum and Dynamics

@article{Bourget2020OnedimensionalDD,
  title={One-dimensional Discrete Dirac Operators in a Decaying Random Potential I: Spectrum and Dynamics},
  author={O. Bourget and Gregorio R. Moreno Flores and Amal Taarabt},
  journal={Mathematical Physics, Analysis and Geometry},
  year={2020},
  volume={23},
  pages={1-51}
}
We study the spectrum and dynamics of a one-dimensional discrete Dirac operator in a random potential obtained by damping an i.i.d. environment with an envelope of type n − α for α > 0. We recover all the spectral regimes previously obtained for the analogue Anderson model in a random decaying potential, namely: absolutely continuous spectrum in the super-critical region α > 1 2 $\alpha >\frac 12$ ; a transition from pure point to singular continuous spectrum in the critical region α = 1 2… 

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