On stability for time-periodic perturbations of harmonic oscillators

Min-Jei Huang

Annales de l'I.H.P. Physique théorique (1989)

  • Volume: 50, Issue: 3, page 229-238
  • ISSN: 0246-0211

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Huang, Min-Jei. "On stability for time-periodic perturbations of harmonic oscillators." Annales de l'I.H.P. Physique théorique 50.3 (1989): 229-238. <http://eudml.org/doc/76446>.

@article{Huang1989,
author = {Huang, Min-Jei},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {harmonic oscillators; monodromy operator; point spectrum},
language = {eng},
number = {3},
pages = {229-238},
publisher = {Gauthier-Villars},
title = {On stability for time-periodic perturbations of harmonic oscillators},
url = {http://eudml.org/doc/76446},
volume = {50},
year = {1989},
}

TY - JOUR
AU - Huang, Min-Jei
TI - On stability for time-periodic perturbations of harmonic oscillators
JO - Annales de l'I.H.P. Physique théorique
PY - 1989
PB - Gauthier-Villars
VL - 50
IS - 3
SP - 229
EP - 238
LA - eng
KW - harmonic oscillators; monodromy operator; point spectrum
UR - http://eudml.org/doc/76446
ER -

References

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  1. [1] J. Bellissard, Stability and Instability in Quantum Mechanics, in Schrödinger Operators, ed. by S. Graffi. Lecture Notes in Mathematics, 1159, Springer-Verlag, Berlin/Heidelberg/New York/Tokyo, 1985. Zbl0581.35078MR853743
  2. [2] M. Combescure, A Quantum Particle in a Quadrupole Radio-Frequency Trap. Ann. Inst. H. Poincaré, Sec. A, t. 44, 1986, p. 293-314. Zbl0613.46064MR846470
  3. [3] M. Combescure, Trapping of Quantum Particles for a class of Time-Periodic Potentials : A Semi-Classical Approach, Ann. of Physics, t. 173, 1987, p. 210-225. Zbl0634.35062MR870892
  4. [4] M. Combescure, The Quantum Stability Problem for Time-Periodic Perturbations of the Harmonic OscillatorAnn. Inst. H. Poincaré, Sec. A, t. 47, 1987, p. 63-83. Zbl0628.70017MR912757
  5. [5] V. Enss and K. Veselic, Bound States and Propagating States for Time-Dependent Hamiltonians. Ann. Inst. H. Poincaré, Sec. A, t. 39, 1983, p. 159-191. Zbl0532.47007MR722684
  6. [6] J.K. Hale, Ordinary Differential Equations, John Wiley and Sons, New York/London/ Sydney, 1969. Zbl0186.40901MR419901
  7. [7] T. Kato, Linear Evolution Equations of Hyperbolic Type, J. Fac. Sci. Univ. Tokyo, Sec. IA, t. 17, 1970, p. 241-258. Zbl0222.47011MR279626
  8. [8] M.G. Krein, On Certain Problems on the Maximum and Minimum of Characteristic Values and the Lyapunov Zones of Stability. Amer. Math. Soc. Transl., t. 1, 1955, p. 163-187. Zbl0066.33404MR73776
  9. [9] M. Reed and B. Simon, Methods of Modern Mathematical Physics, t. 2, Fourier Analysis, Self-Adjointness, Academic Press, New York/San Francisco/London, 1975. Zbl0308.47002
  10. [10] M. Reed and B. Simon, Methods of Modern Mathematical Physics, t. 4, Analysis of Operators, Academic Press, New York/San Francisco/London, 1978. Zbl0401.47001
  11. [11] V.A. Yakubovich and V.M. Starzhinskii, Linear Differential Equations with Periodic Coefficients, t. 2, John Wiley and Sons, New York/Toronto, 1975. 

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