An adiabatic theorem for singularly perturbed hamiltonians

Alain Joye

Annales de l'I.H.P. Physique théorique (1995)

  • Volume: 63, Issue: 2, page 231-250
  • ISSN: 0246-0211

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Joye, Alain. "An adiabatic theorem for singularly perturbed hamiltonians." Annales de l'I.H.P. Physique théorique 63.2 (1995): 231-250. <http://eudml.org/doc/76694>.

@article{Joye1995,
author = {Joye, Alain},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {adiabatic approximation; Hamiltonian; gap assumption; time-dependent perturbation},
language = {eng},
number = {2},
pages = {231-250},
publisher = {Gauthier-Villars},
title = {An adiabatic theorem for singularly perturbed hamiltonians},
url = {http://eudml.org/doc/76694},
volume = {63},
year = {1995},
}

TY - JOUR
AU - Joye, Alain
TI - An adiabatic theorem for singularly perturbed hamiltonians
JO - Annales de l'I.H.P. Physique théorique
PY - 1995
PB - Gauthier-Villars
VL - 63
IS - 2
SP - 231
EP - 250
LA - eng
KW - adiabatic approximation; Hamiltonian; gap assumption; time-dependent perturbation
UR - http://eudml.org/doc/76694
ER -

References

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  1. [AHS] J. Avron, J. Howland and B. Simon, Adiabatic Theorems for Dense Point Spectra, Commun. Math. Phys., Vol. 128, 1990, pp. 497-507. Zbl0711.35101MR1045880
  2. [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. Zbl0626.58033MR885569
  3. [BF] M. Born and V. Fock, Beweis des Adiabatensatzes, Zeit. f. Phys., Vol. 51, 1928, pp. 165-169. Zbl54.0994.03JFM54.0994.03
  4. [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. Zbl0884.47053
  5. [JP2] A. Joye and C. Pfister, Exponentially Small Adiabatic Invariant for the Schroedinger Equation, Commun. Math. Phys., Vol. 140, 1991, pp. 15-41. Zbl0755.35104MR1124257
  6. [Ka1] T. Kato, On the Adiabatic Theorem of Quantum Mechanics, J. Phys. Soc. Japan, Vol. 5, 1950, pp. 435-439. 
  7. [Ka2] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, New York, 1966. Zbl0148.12601MR203473
  8. [Kr] S.G. Krein, Linear Differential Equations in Banach Spaces, American Mathematical Society, Vol. 29, Providence, 1971. MR342804
  9. [N1] G. Nenciu, On the Adiabatic Theorem of Quantum Mechanics, J. Phys.A, Vol. 13, 1980, L15-L18. Zbl0435.47025MR558631
  10. [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. Zbl0726.34077MR1189402
  11. [N3] G. Nenciu, Adiabatic Theorems and Spectral Concentration, Commun. Math. Phys., Vol. 82, 1981, pp. 121-135. Zbl0493.47009MR638516
  12. [RS] M. Reed and B. Simon, Methods of Modem Mathematical Physics, II Fourier Analysis, Self-Adjointness, Academic Press, New York, San Francisco, London, 1975. Zbl0308.47002

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