TY - JOUR
T1 - Anderson Localization for 2D Discrete Schrödinger Operators with Random Magnetic Fields
AU - Klopp, Frédéric
AU - Nakamura, Shu
AU - Nakano, Fumihiko
AU - Nomura, Yuji
PY - 2003
Y1 - 2003
N2 - 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.
AB - 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.
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U2 - 10.1007/s00023-003-0147-3
DO - 10.1007/s00023-003-0147-3
M3 - Article
AN - SCOPUS:0344629398
SN - 1424-0637
VL - 4
SP - 795
EP - 811
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 4
ER -