Analytic approaches to periodically driven closed quantum systems: methods and applications

We present a brief overview of some the analytic perturbative techniques for computation Floquet Hamiltonian periodically driven, or Floquet, quantum many-body system. The key technical points about each methods discussed are presented in pedagogical manner. They followed by account chosen phenomena where these have provided useful insights. provide an extensive discussion Floquet-Magnus expansion, adiabatic-impulse approximation, and perturbation theory. This is relatively short discourse on rotating wave resummation technique flow method. also open problems which may possibly be addressed using methods.