@article{JEDP_2005____A3_0, author = {Fermanian Kammerer, Clotilde and Lasser, Caroline}, title = {An algorithm for quantum propagation through electron level crossings.}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, year = {2005}, pages = {1-14}, doi = {10.5802/jedp.16}, mrnumber = {2352772}, language = {en}, url = {http://dml.mathdoc.fr/item/JEDP_2005____A3_0} }
Fermanian Kammerer, Clotilde; Lasser, Caroline. An algorithm for quantum propagation through electron level crossings.. Journées équations aux dérivées partielles, (2005), pp. 1-14. doi : 10.5802/jedp.16. http://gdmltest.u-ga.fr/item/JEDP_2005____A3_0/
[1] Y. Colin de Verdière: The level crossing problem in semi-classical analysis I. the symmetric case. To appear in the Proceedings of Frédéric Pham’s congress, Annales de l’Institut Fourier, (2002). | Numdam | MR 2033509 | Zbl 02014671
[2] Y. Colin de Verdière: The level crossing problem in semi-classical analysis. II. The hermitian case, To appear in the proceedings of Louis Boutet de Monvel’s congress, Annales de l’Institut Fourier, (2003). | Numdam | MR 2127853 | Zbl 1067.35162
[3] C. Fermanian Kammerer: Wigner measures and molecular propagation through generic energy level crossings, Reviews in Mathematical Physics 15, 2003, 1285–1317. | MR 2038071 | Zbl 1069.81548
[4] C. Fermanian Kammerer, P. Gérard: Mesures semi-classiques et croisements de modes. Bull. Soc. math. France, 130, N1, 2002, 123–168. | Numdam | MR 1906196 | Zbl 0996.35004
[5] C. Fermanian Kammerer, P. Gérard: A Landau-Zener formula for non-degenerated involutive codimension 3 crossings. Ann. Henri Poincaré 4, 2003, 513–552. | MR 2007256 | Zbl 1049.81029
[6] C. Fermanian Kammerer, C. Lasser: Wigner measures and codimension two crossings. Jour. Math. Phys. 44(2), 2003, 507–527. | MR 1952198 | Zbl 1061.81078
[7] C. Fermanian Kammerer, C. Lasser: Modeling of molecular propagation through conical intersection: an algorithm. (preprint).
[8] P. Gérard, P. A. Markowich, N. J. Mauser, F. Poupaud: Homogenization Limits and Wigner Transforms. Comm. Pure Appl. Math. 50(4), 1997, 323–379. | MR 1438151 | Zbl 0881.35099
[9] G. A. Hagedorn: Molecular Propagation through Electron Energy Level Crossings. Memoirs of the A. M. S., 111, N 536, 1994. | MR 1234882 | Zbl 0833.92025
[10] L. Landau: Collected papers of L. Landau, Pergamon Press, 1965.
[11] C. Lasser, S. Teufel: Propagation through conical crossings: An asymptotic semigroup. Comm. Pure Appl. Math. 58(9), 2005, 1188–1230. | MR 2163659 | Zbl 02207891
[12] L. Miller: Propagation d’ondes semi-classiques à travers une interface et mesures 2-microlocales. Thèse de l’Ecole Polytechnique, 1996.
[13] R. Schneider, W. Domcke, H. Köppel: Aspects of dissipative electronic and vibrational dynamics of strongly vibronically coupled sytems. J. Chem. Phys. 92(2), 1990, 1045–1061.
[14] H. Spohn, S. Teufel: Adiabatic decoupling and time-dependent Born-Oppenheimer theory, Commun. Math. Phys. 224, 2001, 113–132. | MR 1868994 | Zbl 1017.81014
[15] J. Tully: Molecular dynamics with electronic transitions. J. Chem. Phys. 93(2), 1990, 1061–1071
[16] E. Wigner: On the quantum correction to thermodynamic equilibrium. Phys. Rev. 40(2), 1932, 749–759. | Zbl 0004.38201
[17] C. Zener: Non-adiabatic crossing of energy levels, Proc. Roy. Soc. Lond. 137, 1932, 696–702. | Zbl 0005.18605