Geodesic
Stark effect for a~difference Schr\"odinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 1, pp. 70-80

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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. 
@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},
     publisher = {mathdoc},
     volume = {78},
     number = {1},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_78_1_a6/}
}
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E. I. Dinaburg. Stark effect for a~difference Schr\"odinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 1, pp. 70-80. http://geodesic.mathdoc.fr/item/TMF_1989_78_1_a6/