The Landau–Zener formula made simple

The approach by Ettore Majorana for non-adiabatic transitions between two quasi-crossing levels is revisited and significantly extended. We rederive the transition probability, known as the Landau–Zener–Stückelberg–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 and Stückelberg. Moreover, we go well beyond previous results and we now obtain the full wave function, including its phase, which is important nowadays for quantum control and quantum information. The asymptotic wave function correctly describes the dynamics away from the avoided-level crossing, while it has limited accuracy in that region.

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

Kofman

Ivakhnenko

Shevchenko

et al. 2023

Sci Rep

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Two potential paths for OH radical formation on surfaces of pure water microdroplets

Skurski,

Simons

2024

The Journal of Chemical Physics

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Experimental findings by others suggest that OH radicals are formed in unexpected abundance on or near surfaces of 1–50 µm microdroplets comprised of pure water, but the mechanism by which these radicals are generated is not yet fully resolved. In this work, we examine two possibilities using ab initio electronic structure methods: (1) electron transfer (ET) from a microdroplet surface-bound OH− anion to a nearby H3O+ cation and (2) proton transfer (PT) from such a H3O+ cation to a nearby OH− anion. Our findings suggest that both processes are possible but only if the droplet’s underlying water molecules comprising the microdroplet provide little screening of the Coulomb interaction between the anion and cation once they reach ∼10 Å of one another. In the ET event, an OH radical is formed directly; for PT, the OH formation occurs because the new O–H bond formed by the transferred proton is created at a bond length sufficiently elongated to permit homolytic cleavage. Both the ET and PT pathways predict that H atoms will also be formed. Finally, we discuss the roles played by strong local electric fields in mechanisms that have previously been proposed and that occur in our two mechanisms.

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Tuning the initial phase to control the final state of a driven qubit

Kofman,

Shevchenko,

Nori

2024

Phys. Rev. A

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The Landau–Zener formula made simple

Cited by 5 publications

References 38 publications

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

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

Two potential paths for OH radical formation on surfaces of pure water microdroplets

Tuning the initial phase to control the final state of a driven qubit

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