Eigenstates of the quantum Penning–Ioffe nanotrap at resonance
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 3, pp. 406-425 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We discuss the choice of physical parameters of a quantum Penning nanotrap under the action of a perturbing inhomogeneous Ioffe magnetic field and also the role of frequency resonance modes. We present a general scheme for constructing the asymptotic behavior of the eigenstates by the generalized geometric quantization method and obtain the reproducing measure in the integral representation of eigenfunctions.
Mots-clés : nanotrap
Keywords: resonance, quantum averaging, symmetry algebra, irreducible representation, reproducing measure.
@article{TMF_2014_179_3_a7,
     author = {M. V. Karasev and E. M. Novikova},
     title = {Eigenstates of the~quantum {Penning{\textendash}Ioffe} nanotrap at resonance},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {406--425},
     year = {2014},
     volume = {179},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a7/}
}
TY  - JOUR
AU  - M. V. Karasev
AU  - E. M. Novikova
TI  - Eigenstates of the quantum Penning–Ioffe nanotrap at resonance
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2014
SP  - 406
EP  - 425
VL  - 179
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a7/
LA  - ru
ID  - TMF_2014_179_3_a7
ER  - 
%0 Journal Article
%A M. V. Karasev
%A E. M. Novikova
%T Eigenstates of the quantum Penning–Ioffe nanotrap at resonance
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2014
%P 406-425
%V 179
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a7/
%G ru
%F TMF_2014_179_3_a7
M. V. Karasev; E. M. Novikova. Eigenstates of the quantum Penning–Ioffe nanotrap at resonance. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 3, pp. 406-425. http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a7/

[1] L. S. Brown, G. Gabrielse, Phys. Rev. A, 25:4 (1982), 2423–2425 | DOI

[2] G. Gabrielse, Phys. Rev. A, 27:5 (1983), 2277–2290 | DOI

[3] G. Gabrielse, Phys. Rev. A, 29:2 (1984), 462–469 | DOI

[4] G. Gabrielse, F. C. Mackintosh, Internat. J. Mass Spectrom. Ion Processes, 57:1 (1984), 1–17 | DOI

[5] G. Gabrielse, L. Haarsma, S. L. Rolston, Internat. J. Mass Spectrom. Ion Processes, 88:2–3 (1989), 319–332 | DOI

[6] G. Gabrielse, H. Dehmelt, “Geonium without a magnetic bottle – a new generation”, Precision Measurement and Fundamental Constants. II, National Bureau of Standards (US), Special Publication, 617, eds. B. N. Taylor, W. D. Phillips, Government Printing Office, Washington, DC, 1984, 219–221

[7] D. Segal, M. Shapiro, Nano Lett., 6:8 (2006), 1622–1626 | DOI

[8] K. Blaum, Yu. N. Novikov, G. Werth, Contemp. Phys., 51:2 (2010), 149–175, arXiv: 0909.1095 | DOI

[9] F. Herfurth, K. Blaum (eds.), Trapped Charged Particles and Fundamental Interactions, Lecture Notes in Physics, 749, Springer, Berlin, 2008 | DOI

[10] P. K. Ghosh, Ion Traps, Clarendon Press, Oxford, 1995

[11] F. G. Major, V. Gheorghe, G. Werth, Charged Particle Traps, Springer, Berlin, 2002

[12] S. Dhar, O. Brandt, M. Ramsteiner, V. F. Sapega, K. H. Ploog, Phys. Rev. Lett., 94:3 (2005), 037205, 4 pp. | DOI

[13] M. V. Karasev, V. P. Maslov, UMN, 39:6(240) (1984), 115–173 | DOI | MR | Zbl

[14] M. V. Karasev, “Birkhoff resonances and quantum ray method”, Proceedings of International Seminar “Days on Diffraction” – 2004 (St. Petersburg, Russia, June 29 – July 2, 2004), Universitas Petropolitana, St. Petersburg, 114–126

[15] M. V. Karasev, “Noncommutative algebras, nano-structures, and quantum dynamics generated by resonances. I”, Quantum Algebras and Poisson Geometry in Mathematical Physics, AMS Translations, Ser. 2, 216, ed. M. V. Karasev, AMS, Providence, RI, 2005, 1–18, arXiv: ; Adv. Stud. Contemp. Math., 11:1 (2005), 33–56 ; Russ. J. Math. Phys., 13:2 (2006), 131–150 math/0412542 | MR | MR | Zbl | DOI | MR | Zbl

[16] M. V. Karasev, E. M. Novikova, “Non-Lie permutation relations, coherent states, and quantum embedding”, Coherent Transform, Quantization, and Poisson Geometry, AMS Translations, Ser. 2, 187, ed. M. V. Karasev, AMS, Providence, RI, 1998, 1–202 | MR | Zbl

[17] M. V. Karasev, Lett. Math. Phys., 56:3 (2001), 229–269 | DOI | MR | Zbl

[18] M. V. Karasev, E. M. Novikova, “Algebras with polynomial commutation relations for a quantum particle in electric and magnetic fields”, Quantum Algebras and Poisson Geometry in Mathematical Physics, AMS Translations, Ser. 2, 216, ed. M. V. Karasev, AMS, Providence, RI, 2005, 19–135 ; М. В. Карасев, Е. М. Новикова, ТМФ, 108:3 (1996), 339–387 | MR | Zbl | DOI | DOI | MR | Zbl

[19] M. V. Karasev, Zap. nauchn. sem. LOMI, 172 (1989), 41–54 ; M. V. Karasev, “Simple Quantization Formula”, Symplectic Geometry and Mathematical Physics (Aix-en-Provence, 1990), Progress in Mathematics, 99, eds. P. Donato, C. Duval, J. Elhadad, G. M. Tuynman, Birkhäuser, Boston, MA, 1991, 234–243 ; Russ. J. Math. Phys., 3:3 (1995), 393–400 | DOI | MR | Zbl | MR | MR | Zbl

[20] M. V. Karasev, E. M. Novikova, J. Math. Sci., 95:6 (1999), 2703–2798 | DOI | MR | Zbl

[21] M. V. Karasev, E. M. Novikova, Russ. J. Math. Phys., 20:3 (2013), 283–294 | DOI | MR | Zbl

[22] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 1, 2, Nauka, M., 1965, 1966 | MR | Zbl

[23] D. J. Fernández, M. Velázquez, J. Phys. A, 42:8 (2009), 085304, 9 pp. | DOI | MR | Zbl

[24] M. Genkin, E. Lindroth, J. Phys. A, 42:27 (2009), 275305, 6 pp. | DOI | MR | Zbl