I will open my talk by explaining the fundamental concept of parametric resonance and giving examples of some practical application (Paul traps, Kapitza pendulum). I will then clarify why the existence of this phenomenon in many-body systems is still debated. Although it is believed that large systems cannot display true parametric resonances, I will overview some exceptions to this general rule. In the last part of the talk, I will describe some new results on the dynamics of periodically-driven many-body quantum systems.

REFERENCES:
Citro etal, Annals of Physics, 360, 694 (2015)
Russomanno and Dalla Torre, arxiv:1510.08866