Landau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation
Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 1, pp. 85-134.
@article{AIHPA_1998__68_1_85_0,
     author = {Hagedorn, George A. and Joye, Alain},
     title = {Landau-Zener transitions through small electronic eigenvalue gaps in the {Born-Oppenheimer} approximation},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {85--134},
     publisher = {Gauthier-Villars},
     volume = {68},
     number = {1},
     year = {1998},
     mrnumber = {1618922},
     zbl = {0915.35090},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1998__68_1_85_0/}
}
TY  - JOUR
AU  - Hagedorn, George A.
AU  - Joye, Alain
TI  - Landau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1998
SP  - 85
EP  - 134
VL  - 68
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1998__68_1_85_0/
LA  - en
ID  - AIHPA_1998__68_1_85_0
ER  - 
%0 Journal Article
%A Hagedorn, George A.
%A Joye, Alain
%T Landau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation
%J Annales de l'I.H.P. Physique théorique
%D 1998
%P 85-134
%V 68
%N 1
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1998__68_1_85_0/
%G en
%F AIHPA_1998__68_1_85_0
Hagedorn, George A.; Joye, Alain. Landau-Zener transitions through small electronic eigenvalue gaps in the Born-Oppenheimer approximation. Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 1, pp. 85-134. http://www.numdam.org/item/AIHPA_1998__68_1_85_0/

[1] J.D. Cole. Perturbation Methods in Applied Mathematics Waltham, Mass., Toronto, London: Blaisdell 1968. | MR | Zbl

[2] J.-M. Combes, On the Born-Oppenheimer Approximation. In: International Symposium on Mathematical Problems in Theoretical Physics. ed. by H. Araki. Berlin, Heidelberg, New York: Springer 1975. | MR

[3] J.-M. Combes, The Born-Oppenheimer Approximation. In: The Schrödinger Equation. ed. by W. Thirring, P. Urban. Wien, New York: Springer 1977. | MR | Zbl

[4] J.-M. Combes, P. Duclos and R. Seiler, The Born-Oppenheimer Approximation. In Rigorous Atomic and Molecular Physics. ed. by G. Velo, A. Wightman. New York: Plenum 1981.

[5] I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products. New York: Academic Press 1980.

[6] G.A. Hagedorn, A Time-Dependent Born-Oppenheimer Approximation. Commun. Math. Phys., Vol. 77, 1980, pp. 1-19. | MR | Zbl

[7] G.A. Hagedorn, Semiclassical Quantum Mechanics IV: Large Order Asymptotics and More General States in More than One Dimension. Ann. Inst. H. Poincaré Sect. A, Vol. 42, 1985, pp. 363-374. | Numdam | MR | Zbl

[8] G.A. Hagedorn, High Order Corrections to the Time-Dependent Born-Oppenheimer Approximation I: Smooth Potentials. Ann. Math., Vol. 124, 1986, pp. 571-590, Erratum, Vol. 126, 1987, p. 219. | MR | Zbl

[9] G.A. Hagedorn, High Order Corrections to the Time-Independent Born-Oppenheimer Approximation I: Smooth Potentials. Ann. Inst. H. Poincaré Sect. A, Vol. 47, 1987, pp. 1-19. | Numdam | MR | Zbl

[10] G.A. Hagedorn, High Order Corrections to the Time-Independent Born-Oppenheimer Approximation II: Diatomic Coulomb Systems. Commun. Math. Phys., Vol. 116, 1988, pp. 23-44. | MR

[11] G.A. Hagedorn, High Order Corrections to the Time-Dependent Born-Oppenheimer Approximation II: Coulomb Systems. Commun. Math. Phys., Vol. 117, 1988, pp. 387-403. | MR

[12] G.A. Hagedorn, Multiple Scales and the Time-Independent Born-Oppenheimer Approximation. In: Differential Equations and Applications. ed. by R. Aftabizadeh. New York: Marcel Dekker 1989. | MR | Zbl

[13] G.A. Hagedorn, Electron Energy Level Crossings in the Time-Dependent Bom-Oppenheimer Approximation. Theor. Chimica Acta., Vol. 77, 1990, pp. 163-190.

[14] G.A. Hagedorn, Proof of the Landau-Zener Formula in an Adiabatic Limit with Small Eigenvalue Gaps. Commun. Math. Phys., Vol. 136, 1991, pp. 433-449. | MR | Zbl

[15] G.A. Hagedorn, Time-Reversal Invariance and the Time-Dependent Born-Oppenheimer Approximation. In Forty More Years of Ramifications: Spectral Asymptotics and Its Applications, (Discourses in Mathematics and Its Applications, No. 1). ed. by S. A. Fulling and F. J. Narcowich. College Station: Texas A & M University Mathematics Department 1992. | Zbl

[16] G.A. Hagedorn, Molecular Propagation Through Electron Energy Level Crossings, Memoirs Amer. Math. Soc., Vol. 536, 1994. | MR | Zbl

[17] G.A. Hagedorn, Effects of Electron Energy Level Crossings on Molecular Propagation. Differential Equations and Mathematical Physics. Proceedings of the International Conference. Univ. of Alabama at Birmingham, March 13-17, 1994. ed by I. Knowles. 1995, pp. 85-95. | MR | Zbl

[18] G.A. Hagedorn, Classification and Normal Forms for Avoided Crossings of Quantum Mechanical Energy Levels. 1995 Preprint, Virginia Polytechnic Institute and State University. | MR

[19] G.A. Hagedorn and A. Joye, Molecular Propagation through Small Avoided Crossings of Electron Energy Levels. 1996 Preprint, Virginia Polytechnic Institute and State University. | MR

[20] J.S. Herrin, The Born-Oppenheimer Approximation: Straight-Up and with a Twist. Ph. D. Dissertation, University of Virginia, 1990.

[21] A. Joye, Non-trivial Prefactors in Adiabatic Transition Probabilities Induced by High Order Complex Degeneracies. J. Phys. A, Vol. 26, 1993, pp. 6517-6540. | MR

[22] A. Joye, Proof of the Landau-Zener Formula. Asymptotic Analysis, Vol. 9, 1994, pp. 209-258. | MR | Zbl

[23] A. Joye, Exponential Asymptotics in a Singular Limit for n-Level Scattering Systems. Preprint CNRS Marseille CPT-95/P.3216, SIAM J. Math. Anal. (to appear). | MR

[24] A. Joye, H. Kunz and C.-E. Pfister, Exponential Decay and Geometric Aspect of Transition Probabilities in the Adiabatic Limit. Ann. Phys., Vol. 208, 1991, pp. 299-332. | MR | Zbl

[25] A. Joye, G. Mileti and C-E. Paster, Interferences in Adiabatic Transition Probabilities Mediated by Stokes Lines. Phys. Rev. A, Vol. 44, 1991, pp. 4280-4295.

[26] A. Joye and C-E.. Pfister, Full Asymptotic Expansion of Transition Probabilities in the Adiabatic Limit. J. Phys. A., Vol. 24, 1991, pp. 753-766. | MR | Zbl

[27] A. Joye and C-E.. Pfister, Absence of Geometrical Correction to the Landau-Zener Formula. Phvs. Lett. A, Vol. 169, 1992, pp. 62-66.

[28] A. Joye and C-E.. Pfister, Superadiabatic Evolution and Adiabatic Transition Probability between Two Non-Degenerate Levels Isolated in the Spectrum. J. Math. Phys., Vol. 34, 1993, pp. 454-479. | MR | Zbl

[29] A. Joye, and C-E.. Pfister, Non-abelian Geometric Effect in Quantum Adiabatic Transitions. Phys. Rev. A, Vol. 48, 1993, pp. 2598-2608. | MR

[30] A. Joye and C-E.. 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

[31 ] A. Joye and C-E.. Pfister, Semi-Classical Asymptotics beyond All Orders for Simple Scattering Systems, SIAM J. Math. Anal., Vol. 26, 1995, pp. 944-977. | MR | Zbl

[32] A. Kargol, The Infinite Time Limit for the Time-Dependent Born-Oppenheimer Approximation. Commun. Math. Phys., Vol. 166, 1994, pp. 129-148. | MR | Zbl

[33] T. Kato, On the Adiabatic Theorem in Quantum Mechanics. J. Phys. Soc. Jpn., Vol. 5, 1950, pp. 435-439.

[34] M. Klein, On the Mathematical Theory of Predissociation. Ann. Phys., Vol. 178, 1987, pp. 48-73. | MR | Zbl

[35] M. Klein, A. Martinez, R. Seiler and X.P. Wang, On the Born-Oppenheimer Expansion for Polyatomic Molecules. Commun. Math. Phys., Vol. 143, 1992, pp. 607-639. | MR | Zbl

[36] M. Klein, A. Martinez and X.P. Wang, On the Born-Oppenheimer Approximation of Wave Operators in Molecular Scattering Theory. Université de Nantes preprint, 1992.

[37] Ph.A. Martin and G. Nenciu, Semi-Classical Inelastic S-Matrix for One-Dimensional N-States Systems, Rev. Math. Phys., Vol. 7, 1995, pp. 193-242. | MR | Zbl

[38] A. Martinez, Développements Asymptotiques et Effet Tunnel dans l'Approximation de Born-Oppenheimer. Ann. Inst. H. Poincaré Sect. A, Vol. 50, 1989, pp. 239-257. | Numdam | MR | Zbl

[39] A. Martinez, Développements Asymptotiques dans l'Approximation de Bom-Oppenheimer. Journées E. D. P. de St. Jean-de-Monts (1988). | Numdam | Zbl

[40] A. Martinez, Resonances dans l'Approximation de Born-Oppenheimer I. J. Diff. Eq., Vol. 91. 1991, pp. 204-234. | MR | Zbl

[41 ] A. Martinez, Resonances dans l'Approximation de Born-Oppenheimer II. Largeur de Résonances. Commun. Math. Phys., Vol. 135, 1991, pp. 517-530. | MR | Zbl

[42] P. Pettersson, WKB Expansions for Systems of Schrödinger Operators with Crossing Eigenvalues. University of Lund PhD Thesis, 1993.