Precise coupling terms in adiabatic quantum evolution: The generic case

Communications in Mathematical Physics

Volumn 260, Issue 2, 2005, Pages 481-509

  Betz, Volker ^a   Teufel, Stefan ^b  

^a INSTITUTE OF EPIDEMIOLOGY   (Germany)

^b UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 26044440215     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-005-1419-1     Document Type: Article

References (20)

1. th printing, New York: Dover, 1972
2. [Ber] Berry, M.V.: Histories of adiabatic quantum transitions. Proc. R. Soc. Lond. A 429, 61-72 (1990)
3. [BerLi] Berry, M.V., Lim, R.: Universal transition prefactors derived by superadiabatic renormalization. J. Phys. A 26, 4737-4747 (1993)
4. 1] Betz, V., Teufel, S.: Precise coupling terms in adiabatic quantum evolution. Annales Henri Poincaré 16, 217-246 (2005)
5. 2] Betz, V., Teufel, S.: Precise coupling terms in adiabatic quantum evolution: extensions and examples. In preparation
6. 3] Betz, V., Teufel, S.: Adiabatic transition histories for Born-Oppenheimer type models. In preparation
7. [BoFo] Born, M., Fock, V.: Beweis des Adiabatensatzes. Zeits. für Phys. 51, 165-169 (1928)
8. [Bo] Boyd, J.P.: The Devil's Invention: Asymptotics, Superasymptotic and Hyperasymptotic Series. Acta Appl. 56, 1-98 (1999)
9. [Di] Dingle, R.B..: Asymptotic Expansions: Their Derivation and Interpretation. New York-London: Academic Press, 1973
10. [HaJo] Hagedorn, G., Joye, A.: Time development of exponentially small non-adiabatic transitions. Commun. Math. Phys. 250, 393-413 (2004)
11. [He] Henrici, P.: Applied and computational analysis, Vol. 2. New York: Wiley, 1977
12. [Jo] Joye, A.: Non-trivial prefactors in adiabatic transition probabilities induced by high order complex degeneracies. J. Phys. A 26, 6517-6540 (1993)
13. [JKP] Joye, A., Kunz, H., Pfister, C.-E.: Exponential decay and geometric aspect of transition probabilities in the adiabatic limit. Ann. Phys. 208, 299 (1991)
14. [JoPf] Joye, A., Pfister, C.-E.: Superadiabatic evolution and adiabatic transition probability between two nondegenerate levels isolated in the spectrum. J. Math. Phys. 34, 454-479 (1993)
15. [Ma] Martinez, A.: Precise exponential estimates in adiabatic theory. J. Math. Phys. 35, 3889-3915 (1994)
16. [LiBe] Lim, R., Berry, M.V.: Superadiabatic tracking of quantum evolution. J. Phys. A 24, 3255-3264 (1991)
17. [Ne] Nenciu, G.: Linear adiabatic theory. Exponential estimates. Commun. Math. Phys. 152, 479-496 (1993)
18. [PST] Panati, G., Spohn, H., Teufel, S.: Space-adiabatic perturbation theory. Adv. Theor. Math. Phys. 7, 145-204 (2003)
19. [Sj] Sjöstrand, J.: Projecteurs adiabatiques du point de vue pseudodifferentiel. C. R. Acad. Sci. Paris Sér. I Math. 317, 217-220 (1993)
20. [Te] Teufel, S.: Adiabatic perturbation theory in quantum dynamics. Springer Lecture Notes in Mathematics 1821, Berlin-Heidelberg-New York: Springer, 2003