Geodesic
Spectrum of three-dimensional landau operator perturbed by a periodic point potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 2, pp. 283-294 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A study is made of a three-dimensional Schrödinger operator with magnetic field and perturbed by a periodic sum of zero-range potentials. In the case of a rational flux, the explicit form of the decomposition of the resolvent of this operator with respect to the spectrum of irreducible representations of the group of magnetic translations is found. In the case of integer flux, the explicit form of the dispersion laws is found, the spectrum is described, and a qualitative investigation of it is made (in particular, it is established that not more than one gap exists). 
@article{TMF_1995_103_2_a8,
     author = {V. A. Geiler and V. V. Demidov},
     title = {Spectrum of three-dimensional landau operator perturbed by a~periodic point potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {283--294},
     year = {1995},
     volume = {103},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a8/}
}
TY  - JOUR
AU  - V. A. Geiler
AU  - V. V. Demidov
TI  - Spectrum of three-dimensional landau operator perturbed by a periodic point potential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1995
SP  - 283
EP  - 294
VL  - 103
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a8/
LA  - ru
ID  - TMF_1995_103_2_a8
ER  - 
%0 Journal Article
%A V. A. Geiler
%A V. V. Demidov
%T Spectrum of three-dimensional landau operator perturbed by a periodic point potential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1995
%P 283-294
%V 103
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a8/
%G ru
%F TMF_1995_103_2_a8
V. A. Geiler; V. V. Demidov. Spectrum of three-dimensional landau operator perturbed by a periodic point potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 2, pp. 283-294. http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a8/

[1] Novikov S. P., Itogi nauki i tekhn. VINITI AN SSSR. Sovrem. problemy matematiki, 23, VINITI, M., 1983, 3–32 | MR | Zbl

[2] Bellissard J., London Math. Soc. Lect. Notes Ser., no. 136, 1988, 49–76 | MR | Zbl

[3] Helffer B., Sjöstrand J., Lect. Notes Phys., 345, 1989, 118–197 | DOI | MR | Zbl

[4] Tsikon Kh., Freze R., Kirsh V., Saimon B., Operatory Shredingera s prilozheniyami k kvantovoi mekhanike i globalnoi geometrii, Mir, M., 1990 | MR

[5] Bete G., Zommerfeld A., Elektronnaya teoriya metallov, OGIZ, M.–L., 1983

[6] Skriganov M. M., Geometricheskie i arifmeticheskie metody v spektralnoi teorii mnogomernykh periodicheskikh operatorov, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, 171, Nauka, L., 1985 | MR | Zbl

[7] Skriganov M. M., Invent. Math., 80:1 (1985), 107–121 | DOI | MR | Zbl

[8] Grigis A., Mohamed A., C. r. Acad. sci. Ser. 1, 315:12 (1992), 1249–1252 | MR | Zbl

[9] Lyskova A. S., TMF, 65:3 (1985), 368–378 | MR

[10] Pavlov B. S., UMN, 42:6 (1987), 99–131 | MR

[11] Albeverio S., Gestezi F., Kheeg-Kron R., Kholden Kh., Reshaemye modeli v kvantovoi mekhanike, Mir, M., 1991 | MR

[12] Grossman A., Hoeg-Krohn R., Mebkhout M., Commun. Math. Phys., 77:1 (1980), 87–110 | DOI | MR

[13] Karpeshina Yu. E., TMF, 57:2 (1983), 304–313 | MR

[14] Zak J., Phys. Rev., 134:6 (1964), A1602–A1611 | DOI | MR

[15] Geiler V. A., Margulis V. A., TMF, 58:3 (1984), 461–472 | MR

[16] Geiler V. A., Margulis V. A., TMF, 61:1 (1984), 140–149 | MR

[17] Geiler V. A., Algebra i analiz, 3:3 (1991), 1–48 | MR

[18] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 4, Mir, M., 1982 | MR

[19] Wannier G. H., Phys. Stat. Sol. (b), 27 (1980), 163–170 | DOI

[20] Zak J., Solid State Phys., 27, eds. H. Ehrenreich et al., 1972, 1–62 | DOI

[21] Lifshits E. M., Pitaevskii L. G., Statisticheskaya fizika, T. 2, Nauka, M., 1978 | MR

[22] Boon M. H., J. Math. Phys., 13:8 (1972), 1268–1285 | DOI | MR

[23] Janssen A., J. Math. Phys., 23:5 (1982), 720–731 | DOI | MR | Zbl

[24] Geiler V. A., Margulis V. A., TMF, 70:2 (1987), 192–201 | MR

[25] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 1, Nauka, M., 1973 | MR

[26] Demkov Yu. N., Ostrovskii V. N., Metod potentsialov nulevogo radiusa v atomnoi fizike, LGU, L., 1975

[27] Van Hove L., Phys. Rev., 89 (1953), 1189–1193 | DOI | MR | Zbl

[28] Colin de Verdier Y., Mem. Soc. Math. France, 1991, no. 46, 99–109 | DOI | Zbl

[29] Pavlov B. S., Smirnov N. V., Zap. nauchn. semin. LOMI, 133, 1984, 197–211 | MR | Zbl

[30] Mironov A. L., Oleinik V. L., TMF, 99:1 (1994), 103–120 | MR | Zbl