# 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…

## 7 Citations

### One-dimensional Discrete Anderson Model in a Decaying Random Potential: from A.C. Spectrum to Dynamical Localization

- Physics, Mathematics
- 2020

We consider a one-dimensional Anderson model where the potential decays in average like $n^{-\alpha}$, $\alpha>0$. This simple model is known to display a rich phase diagram with different kinds of…

### Dynamical Localization for the One-Dimensional Continuum Anderson Model in a Decaying Random Potential

- Physics, MathematicsAnnales Henri Poincaré
- 2020

We consider a one-dimensional continuum Anderson model where the potential decays in average like |x|-α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

### Localization for One-Dimensional Anderson–Dirac Models

- MathematicsAnnales Henri Poincaré
- 2022

We prove spectral and dynamical localization for a one-dimensional Dirac operator to which is added an ergodic random potential, with a discussion on the different types of potential. We use…

### Density of States and Lifshitz Tails for Discrete 1D Random Dirac Operators

- Materials ScienceMathematical Physics, Analysis and Geometry
- 2021

We study the density of states and Lifshitz tails for a family of random Dirac operators on the one-dimensional lattice ℤ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

### S ep 2 02 1 CONTINUUM LIMITS FOR DISCRETE DIRAC OPERATORS ON 2 D SQUARE LATTICES

- Mathematics
- 2021

We discuss the continuum limit of discrete Dirac operators on the square lattice in R as the mesh size tends to zero. To this end, we propose a natural and simple embedding of l(Z h ) into L(R) that…

### Continuum limits for discrete Dirac operators on 2D square lattices

- MathematicsArXiv
- 2021

A natural and simple embedding of l(Z h ) into L(R) that enables us to compare the discreteDirac operators with the continuum Dirac operators in the same Hilbert space L( R) is proposed and strong resolvent convergence is proved.

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