Geodesic
Asymptotic behavior of the spectrum of mixed states for self-consistent field equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 118-127 
M. V. Karasev. Asymptotic behavior of the spectrum of mixed states for self-consistent field equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 1, pp. 118-127. http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a10/
@article{TMF_1984_61_1_a10,
     author = {M. V. Karasev},
     title = {Asymptotic behavior of the spectrum of mixed states for self-consistent field equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {118--127},
     year = {1984},
     volume = {61},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a10/}
}
TY  - JOUR
AU  - M. V. Karasev
TI  - Asymptotic behavior of the spectrum of mixed states for self-consistent field equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 118
EP  - 127
VL  - 61
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a10/
LA  - ru
ID  - TMF_1984_61_1_a10
ER  - 
%0 Journal Article
%A M. V. Karasev
%T Asymptotic behavior of the spectrum of mixed states for self-consistent field equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 118-127
%V 61
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1984_61_1_a10/
%G ru
%F TMF_1984_61_1_a10

Voir la notice de l'article provenant de la source Math-Net.Ru

Classical and quantum action-angle variables are determined for the self-consistent Vlasov equations. Examples of their calculation are given. A reduction of the Vlasov equation with respect to a noncommuting set of first integrals that is closed with respect to the Poisson brackets is constructed. A scheme of semiclassical quantization of the reduced equation is outlined.

[1] Maslov V. P., Teoriya vozmuschenii i asimptoticheskie metody, Nauka, M., 1965 | MR

[2] Langmuir I., Blodgett K., Phys. Rev., 24:1 (1924), 49–59 | DOI

[3] Karasev M. V., Maslov V. P., Sovrem. probl. matem., Itogi nauki i tekhn., VINITI AN SSSR, 13, VINITI, M., 1979, 145–267 | MR

[4] Chernykh S. I., TMF, 52:3 (1982), 491–494 | MR

[5] Maslov V. P., Sovrem. probl. matem., Itogi nauki i tekhn., VINITI SSSR, 11, VINITI, M., 1978, 100–180

[6] Nekhoroshev N. N., Tr. Mosk. matem. ob-va, 26, 1972, 181–198 | MR | Zbl

[7] Weinstein A., Duke Math. J., 44 (1977), 883–892 | DOI | MR | Zbl

[8] Kirillov A. A., UMN, 31:4 (1976), 57–76 | MR | Zbl

[9] Karasev M. V., Usloviya kvantovaniya Maslova v vysshikh kogomologiyakh i analogi ob'ektov teorii Li dlya kanonicheskikh rassloenii simplekticheskikh mnogoobrazii. Ch. I; II, Deponirovano VINITI, No 1092-82 Dep.; No 1093-82 Деп., МИЭМ, М., 1981, 64 с. | MR

[10] Karasev M. V., Maslov V. P., Izv. AN SSSR, ser. matem., 47:5 (1983), 999–1029 | MR | Zbl

[11] Hess H., Lect. Notes Phys., 139, 1981, 1–35 | DOI | MR

[12] Karasev M. V., Maslov V. P., Dokl. AN SSSR, 257:1 (1981), 33–38 | MR | Zbl

[13] Karasev M. V., Maslov V. P., TMF, 53:3 (1982), 374–387 | MR | Zbl

[14] Karasev M. V., Funkts. analiz i ego prilozh., 18:2 (1984), 65–66 | MR | Zbl