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St. Petersburg Mathematical Journal

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Remarks on the quantum adiabatic theorem


Authors: V. S. Buslaev and E. A. Grinina
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 16 (2004), nomer 4.
Journal: St. Petersburg Math. J. 16 (2005), 639-648
MSC (2000): Primary 81Q15
DOI: https://doi.org/10.1090/S1061-0022-05-00870-8
Published electronically: June 21, 2005
MathSciNet review: 2090850
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  • [ASY] J. E. Avron, R. Seiler, and L. G. Yaffe, Adiabatic theorems and applications to the quantum Hall effect, Comm. Math. Phys. 110 (1987), no. 1, 33-49. MR 0885569 (88i:81055)
  • [BF] M. Born and V. Fock, Beweis des Adiabatensatzes, Z. Phys. 51 (1928), 165-169.
  • [DK] Yu. L. Daletskiĭ and M. G. Kreĭn, \cyr Ustoĭchivost′ resheniĭ differentsial′nykh uravneniĭ v banakhovom prostranstve., Izdat. “Nauka”, Moscow, 1970 (Russian). Nonlinear Analysis and its Applications Series. MR 0352638
    Ju. L. Dalec′kiĭ and M. G. Kreĭn, Stability of solutions of differential equations in Banach space, American Mathematical Society, Providence, R.I., 1974. Translated from the Russian by S. Smith; Translations of Mathematical Monographs, Vol. 43. MR 0352639
  • [G] L. M. Garrido, Generalized adiabatic invariance, J. Mathematical Phys. 5 (1964), 355–362. MR 0168283, https://doi.org/10.1063/1.1704127
  • [K] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • [K1] -, On the adiabatic theorem of quantum mechanics, J. Phys. Soc. Japan 5 (1950), 435-439.
  • [K2] S. G. Kreĭn, \cyr Lineĭkhye differentsial′nye uravneniya v Banakhovom prostranstve, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0247239
  • [N] G. Nenciu, On the adiabatic theorem of quantum mechanics, J. Phys. A 13 (1980), no. 2, L15-L18. MR 0558631 (80k:81071)

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Additional Information

V. S. Buslaev
Affiliation: Department of Physics, St. Petersburg State University, Ulyanovskaya 1, Petrodvorets, St. Petersburg 198054, Russia
Email: buslaev@mph.phys.spbu.ru

E. A. Grinina
Affiliation: Department of Physics, St. Petersburg State University, Ulyanovskaya 1, Petrodvorets, St. Petersburg 198054, Russia
Email: kategrin@peterlink.ru

DOI: https://doi.org/10.1090/S1061-0022-05-00870-8
Keywords: Adiabatic theorem, higher order corrections
Received by editor(s): January 14, 2004
Published electronically: June 21, 2005
Additional Notes: Supported by RFBR (grant 02-01-000798).
Article copyright: © Copyright 2005 American Mathematical Society

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