Antiadiabatic theorem for crossing levels

Physics

Scientific paper

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Quantum Mechanics, Zeeman And Stark Effects

Scientific paper

We consider in this note the time dependence of a system for which two levels (which are not in general decoupled) accidentally cross (or almost cross) for some value of the parameters of the Hamiltonian. We show that for a well-defined class of crossings or narrowly avoided crossings, in which the Hamiltonian changes slowly on its own scale, the system will behave oppositely to the usual adiabatic rule.

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