  We explore the statistical properties of energy transfer in ensembles of
doubly-driven Random- Matrix Floquet Hamiltonians, based on universal symmetry
arguments. The energy pumping efficiency distribution P(E) is associated with
the Hamiltonian parameter ensemble and the eigenvalue statistics of the Floquet
operator. For specific Hamiltonian ensembles, P(E) undergoes a transition that
cannot be associated with a symmetry breaking of the instantaneous Hamiltonian.
The Floquet eigenvalue spacing distribution indicates the considered ensembles
constitute generic nonintegrable Hamiltonian families. As a step towards
Hamiltonian engineering, we develop a machine-learning classifier to understand
the relative parameter importance in resulting high conversion efficiency. We
propose Random Floquet Hamiltonians as a general framework to investigate
frequency conversion effects in a new class of generic dynamical processes
beyond adiabatic pumps.
