New physical insights in dynamical stabilization: introducing Periodically Oscillating-Diverging Systems (PODS)

Dynamical stabilization is the ability of a statically diverging stationary state to gain stability by periodically modulating its physical properties in time. This phenomenon is getting recent interest because it is one of the exploited feature of Floquet engineering that develops new exotic states of matter in the quantum realm. Nowadays, dynamical stabilization is done by applying periodic modulations much faster than the natural diverging time of the Floquet systems, allowing for some effective stationary equations to be used instead of the original dynamical system to rationalize the phenomenon. In this work, by combining theoretical models and precision desktop experiments, we show that it is possible to dynamically stabilize a system, in a “synchronized” fashion, by periodically injecting the right amount of external action in a pulse wave manner. Interestingly, the Initial Value Problem underlying this fundamental stability problem is related to the Boundary Value Problem underlying the determination of bound states and discrete energy levels of a particle in a finite potential well, a well-known problem in quantum mechanics. This analogy offers a universal semi-analytical design tool to dynamically stabilize a mass in a potential energy varying in a square-wave fashion.