The exact solution of the multistate LandauZener type model: the generalized bowtie model
Abstract
The generalized bowtie model (Yu N Demkov and V N Ostrovsky 2000 Phys. Rev. A 61 32705) is a particular generalization of the famous twostate LandauZener model widely used in atomic physics and beyond. It comprises an arbitrary number of states; the diabaticpotential 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 nonrigorous reduction of the model to the sequence of twostate transitions. An unusual quasifactorization property of the transition amplitude matrix is established. The entire matrix is expressed via a single complexvalued vector.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 June 2001
 DOI:
 10.1088/09534075/34/12/309
 Bibcode:
 2001JPhB...34.2419D