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Open Access Green as soon as Postprint is submitted to ZB.
Precise Coupling Terms in Adiabatic Quantum Evolution: The Generic Case.
Commun. Math. Phys. 260, 481-509 (2005)
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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Publication type
Article: Journal article
Document type
Scientific Article
ISSN (print) / ISBN
0010-3616
e-ISSN
1432-0916
Quellenangaben
Volume: 260,
Issue: 2,
Pages: 481-509
Publisher
Springer
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)