On the static effective Hamiltonian of a rapidly driven nonlinear system

We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented to arbitrary order, thus overcoming limitations of existing time-dependent perturbation methods and allowing computations that were impossible before. We also provide a simple diagrammatic tool for calculation and treat illustrative examples. By construction, our method applies directly to both quantum and classical systems; the difference is left to a low-level subroutine. This aspect sheds light on the relationship between seemingly disconnected independently developed methods in the literature and has direct applications in quantum engineering.