Berlin 2001 – scientific programme

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A: Atomphysik

A 12: Posters Thursday (Ion/Atom/Molecule/Surface Scattering)

A 12.45: Poster

Thursday, April 5, 2001, 12:30–15:00, AT3

Exact solution of multistate Landau-Zener type model — •Valentin Ostrovsky and Yurii Demkov — Institute of Physics, The University of St Petersburg, 198904 St Petersburg, Russia

Generalized bow-tie model [1] 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. The special restrictions on the model parameters are formulated in Ref. [1]. We derive mathematically rigorous solution of the non-stationary Schrödinger equation for the model by the contour integral method. The approach is similar to that applied to the common bow-tie model [2], but has important distinguishing features. The complete set of state-to-state transition amplitudes is obtained by considering solution asymptotes for t → ± ∞. It agrees with the transition probabilities evaluated earlier [1] by heuristically appealing but non-rigorous reduction of the model to the sequence of two-state transitions. Unusual quasi-factorization property of the transition amplitude matrix is established. The entire matrix is expressed via single complex-valued vector. This feature could be compared with that of another exactly solvable generalization of Landau-Zener model, Demkov-Osherov model [3], where transition matrix is quasi-triangular. The implications of the transition matrix structure are analyzed.

[1] Yu. N. Demkov and V. N. Ostrovsky, Phys. Rev. A 61, 32705 (2000).

[2] V. N. Ostrovsky and H. Nakamura, J. Phys. A 30, 6939 (1997).

[3] Yu. N. Demkov and V. I. Osherov, Sov. Phys.-JETP 26, 916 (1968).