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

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.

Simulating quantum dynamical phenomena using classical oscillators: Landau-Zener-Stückelberg-Majorana interferometry, latching modulation, and motional averaging.

A quantum system can be driven by either sinusoidal, rectangular, or noisy signals. In the literature, these regimes are referred to as Landau-Zener-Stückelberg-Majorana (LZSM) interferometry, latching modulation, and motional averaging, respectively. We demonstrate that these pronounced and interesting effects are also inherent in the dynamics of classical two-state systems. We discuss how such classical systems are realized using either mechanical, electrical, or optical resonators. In addition to the fundamental interest of such dynamical phenomena linking classical and quantum physics, we believe that these are attractive for the classical analogue simulation of quantum systems.