An adiabatic theorem for singularly perturbed hamiltonians
Joye, Alain
Annales de l'I.H.P. Physique théorique, Tome 63 (1995), p. 231-250 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1995-01-01
@article{AIHPA_1995__63_2_231_0,
     author = {Joye, Alain},
     title = {An adiabatic theorem for singularly perturbed hamiltonians},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {63},
     year = {1995},
     pages = {231-250},
     mrnumber = {1357497},
     zbl = {0834.35107},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1995__63_2_231_0}
}

Joye, Alain. An adiabatic theorem for singularly perturbed hamiltonians. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 231-250. http://gdmltest.u-ga.fr/item/AIHPA_1995__63_2_231_0/

[AHS] J. Avron, J. Howland and B. Simon, Adiabatic Theorems for Dense Point Spectra, Commun. Math. Phys., Vol. 128, 1990, pp. 497-507. | MR 1045880 | Zbl 0711.35101

[ASY] J. Avron, R. Seiler and L.G. Yaffe, Adiabatic Theorems and Applications to the Quantum Hall Effect, Commun. Math. Phys., Vol. 110, 1987, pp. 33-49. | MR 885569 | Zbl 0626.58033

[BF] M. Born and V. Fock, Beweis des Adiabatensatzes, Zeit. f. Phys., Vol. 51, 1928, pp. 165-169. | JFM 54.0994.03

[JP1] A. Joye and C. Pfister, Quantum Adiabatic Evolution, in "Leuven Conference Proceedings; On the Three Levels Micro-, Meso, and Macro-approaches in Physics", M. FANNES, C. MEAS, A. VERBEURE, Eds., Plenum, New York, 1994, pp. 139-148. | Zbl 0884.47053

[JP2] A. Joye and C. Pfister, Exponentially Small Adiabatic Invariant for the Schroedinger Equation, Commun. Math. Phys., Vol. 140, 1991, pp. 15-41. | MR 1124257 | Zbl 0755.35104

[Ka1] T. Kato, On the Adiabatic Theorem of Quantum Mechanics, J. Phys. Soc. Japan, Vol. 5, 1950, pp. 435-439.

[Ka2] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, New York, 1966. | MR 203473 | Zbl 0148.12601

[Kr] S.G. Krein, Linear Differential Equations in Banach Spaces, American Mathematical Society, Vol. 29, Providence, 1971. | MR 342804

[N1] G. Nenciu, On the Adiabatic Theorem of Quantum Mechanics, J. Phys. A, Vol. 13, 1980, L15-L18. | MR 558631 | Zbl 0435.47025

[N2] G. Nenciu, Asymptotic Invariant Subspaces, Adiabatic Theorems and Block Diagonalisation, in "Recent Developments in Quantum Mechanics", A. BOUTET DE MONVEL et al., Eds., Kluver Academic Publishers, Dordrecht, 1991. | MR 1189402 | Zbl 0726.34077

[N3] G. Nenciu, Adiabatic Theorems and Spectral Concentration, Commun. Math. Phys., Vol. 82, 1981, pp. 121-135. | MR 638516 | Zbl 0493.47009

[RS] M. Reed and B. Simon, Methods of Modem Mathematical Physics, II Fourier Analysis, Self-Adjointness, Academic Press, New York, San Francisco, London, 1975. | Zbl 0308.47002