Floquet Formalism and Perturbation Theory in the Low-Frequency Limit

Quantum mechanics is one of the most prominent theories in physics today. However, despite being wildly useful, there exist very few exactly solvable quantum problems. Because of this, physicists rely very heavily on theories which provide approximate solutions to those problems which are not exactly solvable, in particulate within the framework of perturbation theory. In this talk, I present a perturbation theory for the low-frequency limit of a periodically-driven quantum system. I compare the corrections to the Rabi problem found using this method to the expansion of its exact solutions to determine the accuracy of the method. I then apply the method to the two-spin Rabi system. I also discuss other extensions and applications of this work to many-body periodically driven systems.