Valentin N. Ostrovsky

Comment on 'Generalization of Keldysh's theory'

We reassess some mathematical aspects of the theory by Keldysh [Sov. Phys. JETP 20, 1307 (1965)]. In particular, we discuss in detail what closed contour is associated with the symbol {integral} introduced by Keldysh and we expose how the contour involved is conveniently deformed to calculate the integral by the saddle-point method. The integral cannot be reduced to a contribution of a single pole that could be evaluated via the residue theorem, contrary to the statement in the recent work by Mishima et al. [Phys. Rev. A 66, 033401 (2002)].

Four-state nonstationary models in multistate Landau-Zener theory

A dynamic four-state system is considered within the context of multistate Landau-Zener theory. It is shown that the theory accounts very well for the time-dependent state populations and final transition probabilities even in cases when multiple crossings appear in close vicinity of each other. This is also true for multiple paths systems when the phases are appropriately accounted for. It is found that transitions may take place also between diabatic states that do not couple directly and that the dynamics of such crossings may be accurately described within the multichannel Landau-Zener theory.