@article{AIHPA_1999__71_1_95_0, author = {Colin de Verdi\`ere, Yves and Lombardi, Maurice and Pollet, Jo\"el}, title = {The microlocal {Landau-Zener} formula}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {95--127}, publisher = {Gauthier-Villars}, volume = {71}, number = {1}, year = {1999}, mrnumber = {1704655}, zbl = {0986.81027}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1999__71_1_95_0/} }
TY - JOUR AU - Colin de Verdière, Yves AU - Lombardi, Maurice AU - Pollet, Joël TI - The microlocal Landau-Zener formula JO - Annales de l'I.H.P. Physique théorique PY - 1999 SP - 95 EP - 127 VL - 71 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1999__71_1_95_0/ LA - en ID - AIHPA_1999__71_1_95_0 ER -
Colin de Verdière, Yves; Lombardi, Maurice; Pollet, Joël. The microlocal Landau-Zener formula. Annales de l'I.H.P. Physique théorique, Tome 71 (1999) no. 1, pp. 95-127. http://www.numdam.org/item/AIHPA_1999__71_1_95_0/
[1] An adiabatic theorem without a gap condition, in: Operator Theory: Advances and Applic., Birkhaüser, 1999, pp. 3-12. | MR | Zbl
and ,[2] Beweis des Adiabatensatzes, Z. Phys. 51 (1928) 165-169. | JFM
and ,[3] Normal forms of real symmetric systems with multiplicity, Indag. Math. 4 (1993) 407-421. | MR | Zbl
and ,[4] Détermination des populations relatives des sous-niveaux magnétiques du niveau 4 1 D de HeI excité par impact d'ions lourds, Journal de Physique 42 (1981) 235-246.
, , , et ,[5] Limite adiabatique en présence de croisements évités et phases géométriques, 1998, en préparation.
,[6] Equilibre instable en regime semi-classique : I - Concentration microlocale, Commun. PDE 19 (1994) 1535-1563. | MR | Zbl
et ,[7] Equilibre instable en régime semi-classique : II - Conditions de Bohr-Sommerfeld, Ann. Inst. Henri Poincaré (Physique théorique) 61 (1994) 347-367. | Numdam | MR | Zbl
et ,[8] Singular Boar-Sommerfeld roles, Commun. Math. Phys., to appear. | MR | Zbl
et ,[9] Le lemme de Morse isochore, Topology 18 (1979) 283-293. | MR | Zbl
et ,[10] Oscillatory integrals with singular symbols, Duke Math. J. 48 (1981) 251-267. | MR | Zbl
and ,[11] Adiabatic expansions near eigenvalue crossings, Ann. Phys. 196 (1989) 278-295. | MR | Zbl
,[12] Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gap, Commun. Math. Phys. 136 (1991) 433-449. | MR | Zbl
,[13] Molecular propagation through electron energy level crossings, Memoirs of the AMS 536 (1994). | MR | Zbl
,[14] Landau-Zener transitions through small electronic eigenvalues gaps in the Born-Oppenheimer approximation, Ann. Inst. Henri Poincaré (Physique théorique) 68 (1998) 85-134. | Numdam | MR | Zbl
and ,[15] Proof of the Landau-Zener formula, Asymptotic Analysis 9 (1994) 209- 258. | MR | Zbl
,[16] Exponential asymptotics in a singular limit for n-level scattering systems, SIAM J. Math. Anal. 28 (1997) 669-703. | MR | Zbl
,[17] Linear Differential Equations in Banach Space, Translations of Math. Monographs, Amer. Math. Soc., 1971. | MR
,[18] Collected Papers of L. Landau, Pergamon Press, 1965.
,[19] Semi-classical inelastic S-matrix for one-dimensional N-states systems, Rev. Math. Phys. 7 (1995) 193-242. | MR | Zbl
and ,[20] Lagrangian intersection and the Cauchy problem, Comm. Pure Appl. Math. 32 (1979) 483-519. | MR | Zbl
and ,[21] Mecanique Quantique, Dunod, 1969. | MR
,[22] Analyse semi-classique d'un système d'équations de Schrödinger couplées : formule de Landau-Zener. Thèse de l'université de Grenoble 1, Octobre 1997.
,[23] Autour de l'Approximation Semi-Classique, Birkhäuser, 1987. | MR | Zbl
,[24] Nonadiabatic effects in slow atomic collisions. I. He+ + He, Phys. Rev. A 4 (1971) 1030-1042.
,[25] Feshbach resonances in the semi-classical limit, Preprint CPT, 1997.
,[26] Helv. Phys. Acta 5 (1932) 369. | Zbl
,[27] Pseudo-differential Operators, Princeton, 1981.
,[28] Asymptotic Expansions for Ordinary Differential Equations, Wiley, New York, 1985. | MR
,[29] Non-adiabatic crossing of energy levels, Proc. Roy. Soc. Lond. 137 (1932) 696-702. | Zbl
,