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

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