Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension
Kostrykin, Vadim ; Schrader, Robert
arXiv, 0005017 / Harvested from arXiv
Text on arXiv
In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.
Publié le : 2000-05-15
Classification:  Mathematical Physics,  (2000 Revision) 82B44,  34F05,  60H25 
@article{0005017,
     author = {Kostrykin, Vadim and Schrader, Robert},
     title = {Global Bounds for the Lyapunov Exponent and the Integrated Density of
  States of Random Schr\"odinger Operators in One Dimension},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0005017}
}

Kostrykin, Vadim; Schrader, Robert. Global Bounds for the Lyapunov Exponent and the Integrated Density of
  States of Random Schr\"odinger Operators in One Dimension. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0005017/