Advertisement

Functional Analysis and Its Applications

, Volume 24, Issue 2, pp 104–114 | Cite as

New global asymptotics and anomalies for the problem of quantization of the adiabatic invariant

  • M. V. Karasev
Article

Keywords

Functional Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    A. S. Bakai and Yu. P. Stepanovskii, Adiabatic Invariants [in Russian], Naukova Dumka, Kiev (1981).Google Scholar
  2. 2.
    M. Born, Lectures on Atomic Mechanics [Russian translation], ONTI, Moscow (1934).Google Scholar
  3. 3.
    L. Schiff, Quantum Mechanics [Russian translation], IL, Moscow (1957).Google Scholar
  4. 4.
    V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], Moscow State Univ. (1965).Google Scholar
  5. 5.
    R. Bott and S. S. Chern, "Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections," Acta Math.,114, 71–112 (1965).Google Scholar
  6. 6.
    B. Simon, "Holonomy, the quantum adiabatic theorem and Berry's phase," Phys. Rev. Lett.,51, 2167–2170 (1965).Google Scholar
  7. 7.
    M. V. Berry, "Quantal phase factors accompanying adiabatic changes," Proc. R. Soc. London,A392, 45–57 (1984).Google Scholar
  8. 8.
    M. V. Berry, "Classical adiabatic angles and quantal adiabatic phase," J. Phys. A, Math. Gen.,18, 15–27 (1985).Google Scholar
  9. 9.
    A. V. Popov, "Transformation of modes for a piecewise analytic waveguide transition (the waveguide approximation)," IZMIRAN, Preprint No. 11 (1978).Google Scholar
  10. 10.
    V. A. Borovikov, "Fields in smoothly irregular waveguides and the problem of the variation of the adiabatic invariant," Inst. Prikl. Mat., Akad. Nauk SSSR, Preprint No. 99 (1978).Google Scholar
  11. 11.
    V. S. Buslaev, "Quasiclassical approximation for equations with periodic coefficients," Usp. Mat. Nauk,42, No. 6, 77–98 (1987).Google Scholar
  12. 12.
    L. V. Berlyand and S. Yu. Dobrokhotov, "Operator separation of variables for problems on short-wave asymptotics of differential equations with quickly oscillating coefficients," Dokl. Akad. Nauk SSSR,297, No. 1, 80–84 (1987).Google Scholar
  13. 13.
    L. D. Faddeev and S. L. Shatashvili, "Algebraic and Hamiltonian methods in the theory of non-Abelian anomalies," Teor. Mat. Fiz.,60, No. 2, 206–217 (1984).Google Scholar
  14. 14.
    M. Jezabek and M. Praszalowics (eds.), Workshop on Skyrmions and Anomalies, World Scientific (1987).Google Scholar
  15. 15.
    M. V. Karasev, "Poisson algebras of symmetries and asymptotic behavior of spectral series," Funkts. Anal. Prilozhen.,20, No. 1, 21–32 (1986).Google Scholar
  16. 16.
    M. V. Karasev, "Connectivities on Lagrange manifolds and some problems of the quasiclassical approximation," Zap. Nauchn. Sem. Leningr. Otd. Mat. Instit. V. A. Steklova,172, 41–54 (1988).Google Scholar
  17. 17.
    M. V. Karasev, "Lagrange rings. Multiscale asymptotics of the spectrum near a resonance," Funkts. Anal. Prilozh.,21, No. 1, 78–79 (1987).Google Scholar
  18. 18.
    M. V. Karasev, "To the Maslov theory of quasiclassical asymptotics. Examples of new global quantization formula applications," ITF, Kiev, Preprint No. ITF-89-78E (1989).Google Scholar
  19. 19.
    M. V. Karasev, "Quantum reduction to the orbits of the symmetry algebra and the Erenfest's problem," ITF, Akad. Nauk Ukr. SSR, Kiev, Preprint No. ITF-87-157R (1987).Google Scholar
  20. 20.
    V. M. Babich, V. S. Buldyrev, and I. A. Molotkov, The Space-Time Ray Method. Linear and Nonlinear Waves [in Russian], Leningrad State Univ. (1985).Google Scholar
  21. 21.
    V. P. Maslov, The Complex WKB Method in Nonlinear Equations [in Russian], Nauka, Moscow (1977).Google Scholar
  22. 22.
    V. I. Arnol'd, "Small denominators and problems of stability of motion in classical and celestial mechanics," Usp. Mat. Nauk,18, No. 6, 91–192 (1963).Google Scholar
  23. 23.
    V. I. Arnol'd, V. V. Kozlov, and A. I. Neidhtadt, "Mathematical aspects of classical and celestial mechanics," in: Current Problems in Mathematics, Fundamental Directions [in Russian], Vol. 3, Vsesoyuz. Inst. Nauchn. Tekhn. Informatsii, Moscow (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • M. V. Karasev

There are no affiliations available

Personalised recommendations