Landau-Zener transition in a multilevel system. An exact result

Details Landau-Zener transition in a multilevel system. An exact result Landau-Zener transition in a multilevel system. An exact result

2003-11-30

arxiv.org/abs/cond-mat/0312011v1

Phys. Rev. A 70, 052708(2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

3 pages, 2 figures

Scientific paper

10.1103/PhysRevA.70.052708

We study the S-matrix for the transitions at an avoided crossing of several energy levels, which is a multilevel generalization of the Landau-Zener problem. We demonstrate that, by extending the Schroedinger evolution to complex time, one can obtain an exact answer for some of the transition amplitudes. Similar to the Landau-Zener case, our result covers both the adiabatic regime (slow evolution.) and the diabatic regime (fast evolution). The form of the exact transition amplitude coincides with that obtained in a sequential pairwise level crossing approximation, in accord with the conjecture of Brundobler and Elser.

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