Localization for one-dimensional Anderson-Dirac models

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 Fürstenberg theorem. We get then the Hölder regularity of the integrated density of states through a new version of Thouless formula, and thus the Wegner estimate necessary for the multiscale analysis.

References in corpus (5)

• The electronic properties of graphene
• Multiscale Analysis and Localization of Random Operators
• Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators
• Hölder continuity of the IDS for matrix-valued Anderson models
• One-dimensional Discrete Dirac Operators in a Decaying Random Potential I: Spectrum and Dynamics