Refined Landau-Zener formulae: Multilevel systems and applications;La formule de Landau-Zener raffinée: Extension aux systèmes multi-niveaux et applications

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 325, Issue 4, 1997, Pages 449-454

  Firica, Gabriel ^a,b  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

^b Department of Theoretical Physics ^*  (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031206399     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(97)85634-0     Document Type: Article

References (16)

1. Beutet de Monvel A. and Nenciu G., 1990. On the theory of adiabatic invariants for linear Hamiltonians systems, C. R. Acad. Sci. Paris, 310, Série I, pp. 807-812.
2. Martin Ph. A. and Nenciu G., 1995. Semi-classical inelastic S-matrix for one-dimensional N-states systems, Rev. Math. Phys., 7, pp..193-242.
3. Joye A., 1994. Proof of Landau-Zener formula, Asymptotic Analysis, 9, pp. 209-258.
4. Hagedorn G., 1989. Adiabatic Expansion near Eigenvalue Crossings, Ann. Phys., 196, pp. 278-295.
5. Ramond T., 1994. Semi-classical study of quantum scattering on the line, Prépublication, 94-18, Université Paris-Nord.
6. Helffer B. and Sjöstrand J., 1990. Semi-classical analysis of Harper's equation III, Mém. Soc. Math. France, No 39.
7. Nenciu G., 1993. Linear Adiabatic Theory. Exponential Estimates, Comm. Math. Phys., 152, pp. 479-496.
8. Martinez A., 1994. Precise exponential estimates in adiabatic theory, J. Math. Phys., 35, pp. 3889-3915.
9. Joye A. and Pfister C.-E., 1991. Exponentially Small Adiabatic Invariant for the Schrödinger Equation, Comm. Math. Phys., 140, pp. 15-41.
10. Pechukas P. and Hwang J.-T., 1977. The Adiabatic Theorem in the Complex Plane and the Semi-Classical Calculation of Non-Adiabatic Transition Amplitudes, J. Chem. Phys., 67, pp. 4640-4653.
11. Hagedorn G., 1991. Proof of the Landau-Zener formula in an Adiabatic Limit with Small Eigenvalue Gaps, Comm. Math. Phys., 136, pp. 433-449.
12. Joye A. and Pfister C.-E., 1993. Superadiabatic Evolution and Adiabatic Transition Probability between Two Non-degenerate Levels Isolated in the Spectrum, J. Math. Phys., 34, pp. 454-479.
13. Joye A., juin 1995. Exponential Asymptotic in a Singular Limit for n-Level Scattering Systems, Preprint CPT-95/P.3216.
14. Firica G. Multilevel adiabatic reduction method: refined Landau-Zener formulae, to appear.
15. Firica G., mai 1995. Refined Landau-Zener formulae: multilevel systems and semi-classical limit of quantum scattering on the line, Preprint de L'Institut de Mathématiques de Paris-Jussieu, U.M.R. 9994, No. 16, (Section 2 is based on the author's graduate thesis performed at the University of Bucharest).
16. Sjöstrand J., 1993. Projecteurs adiabatiques du point de vue pseudo-différentiel, C. R. Acad Sci. Paris, 317, Série I, pp. 217-220.