Geodesic
Stark effect for a difference Schrödinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 1, pp. 70-80 
E. I. Dinaburg. Stark effect for a difference Schrödinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 1, pp. 70-80. http://geodesic.mathdoc.fr/item/TMF_1989_78_1_a6/
@article{TMF_1989_78_1_a6,
     author = {E. I. Dinaburg},
     title = {Stark effect for a~difference {Schr\"odinger} operator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {70--80},
     year = {1989},
     volume = {78},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_78_1_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The tight-binding model of electron motion in an uniform electric field is considered and the spectrum of the corresponding Schrödinger operator perturbed by the potential of an ideal crystallic lattice or the potential rapidly decreasing at infinity. It is shown that for typical directions of the stress vector of the electric field with respect to the basis vectors of the lattice the Schrodinger operator has the purely point and everywhere dense spectrum if the perturbations are small.

[1] Bentosela F., Carmona K., Duclos P., Simon B., Soillard B., Weder R., Commun. Math. Phys., 88:3 (1983), 387–397 | DOI | MR | Zbl

[2] Iensen A., Commun. Math. Phys., 107:1 (1986), 21–28 | DOI | MR

[3] Bellissard J., AC Stark effect in a perfect crystal, Preprint CPT-83/P. 1478, Centre de physique theorique C.N.R.S., Luminy, 1983

[4] Craig W., Commun. Math. Phys., 88:1 (1983), 113–124 | DOI | MR

[5] Pöshell J., Commun. Math. Phys., 88:4 (1983), 447–464 | DOI | MR

[6] Bellissard J., Lima K., Scopolo E., Commun. Math. Phys., 88:4 (1983), 465–478 | DOI | MR

[7] Arnold V. I., UMN, XVIII:6 (1963), 91–192 | MR | Zbl

[8] Bogolyubov N. N., Mitropolskii Yu. A., Samoilenko A. M., Metod uskorennoi skhodimosti v nelineinoi mekhanike, Naukova dumka, Kiev, 1969 | MR

[9] Belokolos E. D., TMF, 25:3 (1975), 344–357 | MR

[10] Dinaburg E. I., Sinai Ya. G., Funkts. analiz i ego prilozh., 9:4 (1975), 8–21 | MR | Zbl