Precise coupling terms in adiabatic quantum evolution: The generic case
Betz, Volker ; Teufel, Stefan
arXiv, 0411083 / Harvested from arXiv
Text on arXiv
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. 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 [Ber] predictions on the universal form of adiabatic transition histories.
Publié le : 2004-11-29
Classification:  Mathematical Physics,  Mathematics - Classical Analysis and ODEs,  34M40,  81Q15,  41A60,  34E05 
@article{0411083,
     author = {Betz, Volker and Teufel, Stefan},
     title = {Precise coupling terms in adiabatic quantum evolution: The generic case},
     journal = {arXiv},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0411083}
}

Betz, Volker; Teufel, Stefan. Precise coupling terms in adiabatic quantum evolution: The generic case. arXiv, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/0411083/