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Precise coupling terms in adiabatic quantum evolution | | Volker Betz
; Stefan Teufel
; | | Date: |
7 Apr 2004 | | Subject: | Mathematical Physics MSC-class: 81Q15 (Primary) 34E05 (Secondary) | math-ph math.MP | | Abstract: | It is known that 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. For a family of two-state systems with real-symmetric Hamiltonian we construct such a superadiabatic representation and explicitly determine the asymptotic behavior of the exponentially small coupling term. First order perturbation theory in the superadiabatic representation then allows us to describe the time-development of exponentially small adiabatic transitions. The latter result rigorously confirms the predictions of Sir Michael Berry for our family of Hamiltonians and slightly generalizes a recent mathematical result of George Hagedorn and Alain Joye. | | Source: | arXiv, math-ph/0404021 | | Services: | Forum | Review | PDF | Favorites | |
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