Localization for one-dimensional Anderson-Dirac models
Mathematical Physics
2023-07-06 v2 Classical Analysis and ODEs
math.MP
Spectral Theory
Abstract
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 scattering properties to prove the positivity of the Lyapunov exponent through F\"urstenberg theorem. We get then the H\"older regularity of the integrated density of states through a new version of Thouless formula, and thus the Wegner estimate necessary for the multiscale analysis.
Cite
@article{arxiv.2109.14246,
title = {Localization for one-dimensional Anderson-Dirac models},
author = {Sylvain Zalczer},
journal= {arXiv preprint arXiv:2109.14246},
year = {2023}
}