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arXiv · 2208.00481

Majorana's approach to nonadiabatic transitions validates the adiabatic-impulse approximation

Polina O. Kofman·Oleh V. Ivakhnenko·Sergey N. Shevchenko·Franco Nori
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Abstract

The approach by Ettore Majorana for non-adiabatic transitions between two quasi-crossing levels is revisited. We rederive the transition probability, known as the Landau-Zener-St\"{u}ckelberg-Majorana formula, and introduce Majorana's approach to modern readers. This result typically referred as the Landau-Zener formula, was published by Majorana before Landau, Zener, St\"{u}ckelberg. Moreover, we obtain the full wave function, including its phase, which is important nowadays for quantum control and quantum information. The asymptotic wave function correctly describes dynamics far from the avoided-level crossing, while it has limited accuracy in that region.

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Polina O. Kofman, Oleh V. Ivakhnenko, Sergey N. Shevchenko, Franco Nori. 2022-07-31. Majorana's approach to nonadiabatic transitions validates the adiabatic-impulse approximation. https://doi.org/10.1038/s41598-023-31084-y

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