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arXiv · cond-mat/0312011

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

A. V. Shytov
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Abstract

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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A. V. Shytov. 2003-11-30. Landau-Zener transition in a multilevel system. An exact result. https://doi.org/10.1103/physreva.70.052708

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