Anderson Localization for 2D Discrete Schrödinger Operators with Random Magnetic Fields

Frédéric Klopp, Shu Nakamura, Fumihiko Nakano, Yuji Nomura

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

We prove Anderson localization near the bottom of the spectrum for two-dimensional discrete Schrödinger operators with random magnetic fields and no scalar potentials. We suppose the magnetic fluxes vanish in pairs, and the magnetic field strength is bounded from below by a positive constant. Main lemmas are the Lifshitz tail and the Wegner estimate on the integrated density of states. Then, Anderson localization, i.e., pure point spectrum with exponentially decreasing eigenfunctions, is proved by the standard multiscale argument.

Original languageEnglish
Pages (from-to)795-811
Number of pages17
JournalAnnales Henri Poincare
Volume4
Issue number4
DOIs
Publication statusPublished - 2003

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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