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Betz, V. ; Teufel, S.

Precise Coupling Terms in Adiabatic Quantum Evolution: The Generic Case.

Commun. Math. Phys. 260, 481-509 (2005)
DOI
Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
For multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. Based on results from [BeTe1] for special Hamiltonians we explicitly determine the asymptotic behavior of the exponentially small coupling term for generic two-state systems with real-symmetric Hamiltonian. The superadiabatic coupling term takes a universal form and depends only on the location and the strength of the complex singularities of the adiabatic coupling function. Our proof is based on a new norm which allows to rigorously implement Darboux' principle, a heuristic guideline widely used in asymptotic analysis. As shown in [BeTe1], first order perturbation theory in the superadiabatic representation then allows to describe the time-development of exponentially small adiabatic transitions and thus to rigorously confirm Michael Berry's [Be] predictions on the universal form of adiabatic transition histories.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
ISSN (print) / ISBN 0010-3616
e-ISSN 1432-0916
Zeitschrift Communications in Mathematical Physics
Quellenangaben Band: 260, Heft: 2, Seiten: 481-509 Artikelnummer: , Supplement: ,
Verlag Springer
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Biomathematics and Biometry (IBB)