Localization for quasi-one-dimensional Dirac operators
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917685920530432 |
|---|---|
| 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 |