Non-adiabatic transitions in multilevel systems appear various fields of physics, but it is not easy to analyze their dynamics general. In this paper, we propose extend the adiabatic impulse approximation systems. This method shown be equivalent a series unitary evolutions and facilitates evaluate numerically. particular, Landau-Zener grid model Landau-Zener-St\"uckelberg-Majorana interference ...

Modern manufacturing faces extensive technological and economic challenges to remain competitive under the current political social conditions [...]