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<p>We consider a random family of Dirac operators on <i>N</i> 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 <i>N</i>.</p>

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Localization for Random Quasi-One-Dimensional Dirac Operators

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Hakim Boumaza,
  • Sylvain Zalczer

摘要

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.