The model of a level crossing with a Coulomb band: exact probabilities of nonadiabatic transitions

Abstract

We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. Our model corresponds to the case of a single linear diabatic energy level interacting with a band of an arbitrary N states, for which the diabatic energies decay with time according to the Coulomb law. We show that the time-dependent Schroedingier equation for this system can be solved in terms of Meijer functions whose asymptotics at a large time can be compactly written in terms of elementary functions that depend on the roots of an Nth order characteristic polynomial. Our model can be considered a generalization of the Demkov-Osherov model. In comparison to the latter, our model allows one to explore the role of curvature of the band levels and diabatic avoided crossings.

18 pages, 3 figures

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Cited by in corpus (3)

• Integrable time-dependent quantum Hamiltonians
• Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets
• Exact results for models of multichannel quantum nonadiabatic transitions