An algorithm for quantum propagation through electron level crossings.

Clotilde Fermanian Kammerer[1]; Caroline Lasser[2]

  • [1] Université de Cergy-Pontoise, Mathématiques, 2 avenue Adolphe Chauvin, BP 222, Pontoise, 95 302 Cergy-Pontoise cedex, France.
  • [2] Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Deutschland.

Journées Équations aux dérivées partielles (2005)

  • page 1-14
  • ISSN: 0752-0360

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Fermanian Kammerer, Clotilde, and Lasser, Caroline. "An algorithm for quantum propagation through electron level crossings.." Journées Équations aux dérivées partielles (2005): 1-14. <http://eudml.org/doc/10610>.

@article{FermanianKammerer2005,
affiliation = {Université de Cergy-Pontoise, Mathématiques, 2 avenue Adolphe Chauvin, BP 222, Pontoise, 95 302 Cergy-Pontoise cedex, France.; Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Deutschland.},
author = {Fermanian Kammerer, Clotilde, Lasser, Caroline},
journal = {Journées Équations aux dérivées partielles},
keywords = {molecule pyrazine ; Schrödinger equation; Wigner transform},
language = {eng},
month = {6},
pages = {1-14},
publisher = {Groupement de recherche 2434 du CNRS},
title = {An algorithm for quantum propagation through electron level crossings.},
url = {http://eudml.org/doc/10610},
year = {2005},
}

TY - JOUR
AU - Fermanian Kammerer, Clotilde
AU - Lasser, Caroline
TI - An algorithm for quantum propagation through electron level crossings.
JO - Journées Équations aux dérivées partielles
DA - 2005/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 14
LA - eng
KW - molecule pyrazine ; Schrödinger equation; Wigner transform
UR - http://eudml.org/doc/10610
ER -

References

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  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). Zbl1113.35151MR2033509
  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). Zbl1067.35162MR2127853
  3. C. Fermanian Kammerer: Wigner measures and molecular propagation through generic energy level crossings, Reviews in Mathematical Physics15, 2003, 1285–1317. Zbl1069.81548MR2038071
  4. C. Fermanian Kammerer, P. Gérard: Mesures semi-classiques et croisements de modes. Bull. Soc. math. France, 130, N o 1, 2002, 123–168. Zbl0996.35004MR1906196
  5. C. Fermanian Kammerer, P. Gérard: A Landau-Zener formula for non-degenerated involutive codimension 3 crossings. Ann. Henri Poincaré4, 2003, 513–552. Zbl1049.81029MR2007256
  6. C. Fermanian Kammerer, C. Lasser: Wigner measures and codimension two crossings. Jour. Math. Phys.44(2), 2003, 507–527. Zbl1061.81078MR1952198
  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. Zbl0881.35099MR1438151
  9. G. A. Hagedorn: Molecular Propagation through Electron Energy Level Crossings. Memoirs of the A. M. S., 111, N o 536, 1994. Zbl0833.92025MR1234882
  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. Zbl1161.35338MR2163659
  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. Zbl1017.81014MR1868994
  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. Zbl0004.38201
  17. C. Zener: Non-adiabatic crossing of energy levels, Proc. Roy. Soc. Lond.137, 1932, 696–702. Zbl0005.18605

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