The exact solution of the multistate Landau-Zener type model: the generalized bow-tie model
Abstract
The generalized bow-tie model (Yu N Demkov and V N Ostrovsky 2000 Phys. Rev. A 61 32705) is a particular generalization of the famous two-state Landau-Zener model widely used in atomic physics and beyond. It comprises an arbitrary number of states; the diabatic-potential curves are linear functions of time whereas the coupling matrix elements are constant. We derive a rigorous solution of the model by the contour integral method. The complete set of transition amplitudes is obtained by considering solution asymptotes for t→±∞. It agrees with the transition probabilities evaluated earlier by heuristically appealing but non-rigorous reduction of the model to the sequence of two-state transitions. An unusual quasi-factorization property of the transition amplitude matrix is established. The entire matrix is expressed via a single complex-valued vector.
- Publication:
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Journal of Physics B Atomic Molecular Physics
- Pub Date:
- June 2001
- DOI:
- 10.1088/0953-4075/34/12/309
- Bibcode:
- 2001JPhB...34.2419D