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New insights on the dynamic stability of time-periodic systems
Periodically time-varying systems are a class of mathematical problems that underlie many important phenomena and applications in physics, such as parametric instabilities,
acoustic tweezers, mass spectrometers and Paul traps or any Floquet engineered systems in Quantum Mechanics. Eventually, the mechanics underlying these problems is fundamentally understood by studying the dynamic stability of a particle in a potential energy landscape that is periodically varying with time, i.e. a dynamical system with a non conservative Hamiltonian.
We present here such a fundamental model, both experimentally and theoretically, and show new appealing results when the variation of energy landscape is large and happens in a time scale similar to the one of the particle. Although in this case, classical approaches such as perturbation theories at play in parametric instabilities or Kapitza dynamical stabilization are no more useful, it is still possible to establish elementary synchronization rules that should be of interest for new promising functionalities in stability and dynamical system theory. Notably, looking for an optimal fashion to stabilize or trap a mass in a strongly oscillating energy field can actually be done by using fundamental mathematical rules of quantum physics.