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Sasaki, Shinji

A bifurcation phenomenon of Stokes curves around a double turning point, and influence of virtual turning points upon the transition probabilities for three-level systems. (English) Zbl 1358.34099

Adv. Math. 301, 711-738 (2016).
In this paper the author discusses non-adiabatic transition problems of three-level systems from the viewpoint of the exact WKB analysis. Using some concrete examples, he points out that a bifurcation phenomenon of Stokes curves around a double turning point plays an important role in computing the transition probabilities. After making an explicit and detailed analysis of such a bifurcation phenomenon, he examines the influence of virtual turning points and new Stokes curves, which are peculiar to multi-level systems, upon transition probabilities.
Reviewer: Yoshitsugu Takei (Kyoto)

Cited in 2 Documents

MSC:

34M40 Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain
34M60 Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent)
34M25 Formal solutions and transform techniques for ordinary differential equations in the complex domain

Keywords:

non-adiabatic transition; three-level system; exact WKB analysis; virtual turning point; new Stokes curve
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References:

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