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Localization for quasi-one-dimensional Dirac operators

Boumaza, Hakim; Zalczer, Sylvain 1
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)

Abstract:

We consider a random family of Dirac operators on $N$ parallel real lines with an ergodic matrix-valued random potential. We establish a criterion for Anderson and dynamical localization involving properties on the group generated by transfer matrices. In particular, we consider not only the usual 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 $N$.


Volltext §
DOI: 10.5445/IR/1000169573
Veröffentlicht am 25.03.2024
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 03.2024
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000169573
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 47 S.
Serie CRC 1173 Preprint ; 2024/9
Projektinformation SFB 1173/3 (DFG, DFG KOORD, SFB 1173/3)
Externe Relationen Siehe auch
Schlagwörter Anderson localization, Dirac operators, random matrices, Lyapunov exponents
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