Adiabatic theory : stability of systems with increasing gaps

G. Nenciu

Annales de l'I.H.P. Physique théorique (1997)

  • Volume: 67, Issue: 4, page 411-424
  • ISSN: 0246-0211

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Nenciu, G.. "Adiabatic theory : stability of systems with increasing gaps." Annales de l'I.H.P. Physique théorique 67.4 (1997): 411-424. <http://eudml.org/doc/76774>.

@article{Nenciu1997,
author = {Nenciu, G.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Schrödinger operator; time dependent perturbation; quantum stability; Floquet operator},
language = {eng},
number = {4},
pages = {411-424},
publisher = {Gauthier-Villars},
title = {Adiabatic theory : stability of systems with increasing gaps},
url = {http://eudml.org/doc/76774},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Nenciu, G.
TI - Adiabatic theory : stability of systems with increasing gaps
JO - Annales de l'I.H.P. Physique théorique
PY - 1997
PB - Gauthier-Villars
VL - 67
IS - 4
SP - 411
EP - 424
LA - eng
KW - Schrödinger operator; time dependent perturbation; quantum stability; Floquet operator
UR - http://eudml.org/doc/76774
ER -

References

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  1. [1] J.A. Baeta Segundo, H. Hey and W. Wreszinski, On quantum stability for systems under quasiperiodic perturbations. To appear in J. Stat. Phys. Zbl0840.58050MR1298110
  2. [2] J. Bellissard, Stability and instability in Quantum Mechanics. In: Schrodinger operators, S. GRAFFI (ed), LNM, Vol. 1159, Springer, Berlin1985. Zbl0581.35078MR824989
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  4. [4] M. Combescure, Recurrent versus diffusive dynamics for a kicked quantum oscillator, Ann. Inst. Henri Poincaré, Phys. Theor., Vol. 57, 1992, p. 67. Zbl0766.58061MR1176358
  5. [5] P. Duclos and P. Stovicek, Floquet Hamiltonians with Pure Point Spectrum, Commun. Math. Phys., Vol. 177, 1996, pp. 327-347. Zbl0848.34072MR1384138
  6. [6] J. Howland, Quantum stability. In: Schrodinger operators. E. BALSLEV (ed), LNP, Vol. 403, 1992, Springer, Berlin. Zbl0784.47056MR1181243
  7. [7] H.R. Jauslin, Stability and chaos in classical and quantum hamiltonian systems. In: II Granada seminar on computational physics. P. GARRIDO and J. MARRO (eds), World Scientific, Singapore1993. MR1349116
  8. [8] J. Howland, Floquet operators with singular spectrum. I. Ann. Inst. Henri Poincare, Phys. Theor., Vol. 50, 1989, pp. 309-323, II. Ann. Inst. Henri Poincaré: Phys. Theor., Vol. 50, 1989, pp. 325-334. Zbl0689.34022MR1017967
  9. [9] J. Howland, Stability of quantum oscillators, J. Phys., Vol. A 25, 1992, pp. 5177-5181. Zbl0764.58039MR1184303
  10. [10] G. Nenciu, Floquet operators without absolutely continuous spectrum. Ann. Inst. Henri Poincaré: Phys. Theor., Vol. 59, 1993, pp. 91-97. Zbl0795.47032MR1244183
  11. [11] A. Joye, Absence of absolutely continuous spectrum of Floquet operators. J. Stat. Phys. , Vol. 75, 1994, pp. 929- 952. Zbl0835.47010MR1285294
  12. [12] G. Nenciu and Rasche, Adiabatic theorem and Gell-Mann-Low formula. H. P. A., Vol. 62, 1989, pp. 372-388. MR1005671
  13. [13] G. Nenciu, Asymptotic invariant subspaces, adiabatic theorems and block diagonalisation. In: BOUTET DE MONVEL et al. (eds), Recent developments in quantum mechanics, pp. 133-149, Dordrecht: Kluver1991. Zbl0726.34077MR1189402
  14. [14] S.G. Krein, Linear differential equations in Banach spaces, Translations of Mathematical Monographs., Vol. 29, 1971, Providence. MR342804
  15. [15] M.S. Birman and M.G. Krein, On the theory of wave operators and scattering theory, Sov. Math. Dokl., Vol. 3, 1962, pp. 740-744. Zbl0196.45004

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