Multipath interference in a multistate Landau-Zener-type model

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 3, 2000, Pages 327051-3270514

  Demkov, Yu N ^a   Ostrovsky, V N ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

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EID: 0004553869     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

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15. Solution of the Demkov-Osherov model was rederived using an alternative method by Y. Kayanuma and S. Fukuchi, [J. Phys. B 18, 4089 (1985)], namely by summing the series of nonstationary perturbation theory in the basis of diabatic states. However, this technique was developed only for the single probability that the system remains at the initially populated slanted diabatic state (cf. Sec. VI B). Note that these authors incorrectly classified the exact solution provided by Demkov and Osherov [10] as approximate. Demkov and Osherov solved exactly their model also in the case where time is replaced by some quantum coordinate (mathematically this amounts to replacing in the Schrödinger equation the first- order derivative in time by the second order derivative over this coordinate). The validity of their solution was recently unjustly questioned by V.A. Yurovsky and A. Ben-Reuven [J. Phys. B 31, 1 (1998)]. This paper pays special attention to the situation where two (or more) horizontal potential curves are degenerate that only rather trivially differs from the nondegenerate case. Indeed, one can always construct linear transformations within the subspace of degenerate states that fully decouples all of them except one, thus reducing the problem to the nondegenerate case.
16. Solution of the Demkov-Osherov model was rederived using an alternative method by Y. Kayanuma and S. Fukuchi, [J. Phys. B 18, 4089 (1985)], namely by summing the series of nonstationary perturbation theory in the basis of diabatic states. However, this technique was developed only for the single probability that the system remains at the initially populated slanted diabatic state (cf. Sec. VI B). Note that these authors incorrectly classified the exact solution provided by Demkov and Osherov [10] as approximate. Demkov and Osherov solved exactly their model also in the case where time is replaced by some quantum coordinate (mathematically this amounts to replacing in the Schrödinger equation the first-order derivative in time by the second order derivative over this coordinate). The validity of their solution was recently unjustly questioned by V.A. Yurovsky and A. Ben-Reuven [J. Phys. B 31, 1 (1998)]. This paper pays special attention to the situation where two (or more) horizontal potential curves are degenerate that only rather trivially differs from the nondegenerate case. Indeed, one can always construct linear transformations within the subspace of degenerate states that fully decouples all of them except one, thus reducing the problem to the nondegenerate case.
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