Localization for random perturbations of periodic Schroedinger operators with regular Floquet eigenvalues
Veselic', Ivan
arXiv, 0510063 / Harvested from arXiv
We prove a localization theorem for continuous ergodic Schr\"odinger operators $ H_\omega := H_0 + V_\omega $, where the random potential $ V_\omega $ is a nonnegative Anderson-type perturbation of the periodic operator $ H_0$. We consider a lower spectral band edge of $ \sigma (H_0) $, say $ E= 0 $, at a gap which is preserved by the perturbation $ V_\omega $. Assuming that all Floquet eigenvalues of $ H_0$, which reach the spectral edge 0 as a minimum, have there a positive definite Hessian, we conclude that there exists an interval $ I $ containing 0 such that $ H_\omega $ has only pure point spectrum in $ I $ for almost all $ \omega $.
Publié le : 2005-10-17
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  35J10, 47B80, 82B44
@article{0510063,
     author = {Veselic', Ivan},
     title = {Localization for random perturbations of periodic Schroedinger operators
  with regular Floquet eigenvalues},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0510063}
}
Veselic', Ivan. Localization for random perturbations of periodic Schroedinger operators
  with regular Floquet eigenvalues. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0510063/