- 04-400 Volker Betz, Stefan Teufel
- Precise coupling terms in adiabatic quantum evolution:
The generic case.
Nov 29, 04
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Abstract. 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.