Discrete Bethe-Sommerfeld Conjecture
Han, Rui ; Jitomirskaya, Svetlana
arXiv, 1707.03482 / Harvested from arXiv
Text on arXiv
In this paper, we prove a discrete version of the Bethe-Sommerfeld conjecture. Namely, we show that the spectra of multi-dimensional discrete periodic Schr\"odinger operators on $\mathbb{Z}^d$ lattice with sufficiently small potentials contain at most two intervals. Moreover, the spectrum is a single interval, provided one of the periods is odd, and can have a gap whenever all periods are even.
Publié le : 2017-07-11
Classification:  Mathematical Physics,  Mathematics - Spectral Theory 
@article{1707.03482,
     author = {Han, Rui and Jitomirskaya, Svetlana},
     title = {Discrete Bethe-Sommerfeld Conjecture},
     journal = {arXiv},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1707.03482}
}

Han, Rui; Jitomirskaya, Svetlana. Discrete Bethe-Sommerfeld Conjecture. arXiv, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/1707.03482/