Geodesic
Particle capture by a slowly varying periodic potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 3, pp. 401-414 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Particle capture by a slowly varying one-dimensional periodic potential is studied by the method of averaging [1]. For large time intervals $t\sim 1/\alpha$ ($\alpha$ is the small parameter which characterizes the rate of change of the potential), including the point of intersection of the separatrix, the solution is constructed up to the first correction terms of order relative to the leading term. The increment $\Delta I$ of the action in a complete evolution interval is also calculated in the leading order in $\alpha$. 
@article{TMF_1986_68_3_a7,
     author = {A. N. Vasil'ev and M. A. Guzev},
     title = {Particle capture by a~slowly varying periodic potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {401--414},
     year = {1986},
     volume = {68},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_68_3_a7/}
}
TY  - JOUR
AU  - A. N. Vasil'ev
AU  - M. A. Guzev
TI  - Particle capture by a slowly varying periodic potential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1986
SP  - 401
EP  - 414
VL  - 68
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1986_68_3_a7/
LA  - ru
ID  - TMF_1986_68_3_a7
ER  - 
%0 Journal Article
%A A. N. Vasil'ev
%A M. A. Guzev
%T Particle capture by a slowly varying periodic potential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1986
%P 401-414
%V 68
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1986_68_3_a7/
%G ru
%F TMF_1986_68_3_a7
A. N. Vasil'ev; M. A. Guzev. Particle capture by a slowly varying periodic potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 3, pp. 401-414. http://geodesic.mathdoc.fr/item/TMF_1986_68_3_a7/

[1] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[2] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1979 | MR

[3] Lenard A., Ann. Phys., 6:3 (1959), 261–276 | DOI | MR | Zbl

[4] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, M., 1981 | MR | Zbl

[5] Timofeev A. V., ZhETF, 75:4 (1978), 1303–1308 | MR