Precise coupling terms in adiabatic quantum evolution

Details Precise coupling terms in adiabatic quantum evolution Precise coupling terms in adiabatic quantum evolution

2004-04-07

arxiv.org/abs/math-ph/0404021v1

Physics

Mathematical Physics

24 pages

Scientific paper

10.1007/s00023-005-0204-1

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.

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