Localization for quasi-one-dimensional Dirac operators

Fuente: arXiv
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Main Authors: Boumaza, Hakim, Zalczer, Sylvain
Format: Preprint
Published: 2024
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author Boumaza, Hakim
Zalczer, Sylvain
author_facet Boumaza, Hakim
Zalczer, Sylvain
contents We consider a random family of Dirac operators on $N$ parallel real lines, modelling for example a graphene nanoribbon. We establish a localization criterion involving properties on the group generated by transfer matrices. In particular, we consider not only the case where this group is the symplectic group but also a strict subgroup of it. We establish under quite general hypotheses that the sum of the Lyapunov exponents and the integrated density of states are Hölder continuous. Moreover, for a set of concrete cases where the potentials are on Pauli matrices, we compute the transfer matrices and prove either localization or delocalization, depending on the potential and on the parity of $N$.
format Preprint
id arxiv_https___arxiv_org_abs_2403_15381
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Localization for quasi-one-dimensional Dirac operators
Boumaza, Hakim
Zalczer, Sylvain
Mathematical Physics
Dynamical Systems
Spectral Theory
We consider a random family of Dirac operators on $N$ parallel real lines, modelling for example a graphene nanoribbon. We establish a localization criterion involving properties on the group generated by transfer matrices. In particular, we consider not only the case where this group is the symplectic group but also a strict subgroup of it. We establish under quite general hypotheses that the sum of the Lyapunov exponents and the integrated density of states are Hölder continuous. Moreover, for a set of concrete cases where the potentials are on Pauli matrices, we compute the transfer matrices and prove either localization or delocalization, depending on the potential and on the parity of $N$.
title Localization for quasi-one-dimensional Dirac operators
topic Mathematical Physics
Dynamical Systems
Spectral Theory
url https://arxiv.org/abs/2403.15381