Energy transfer in random-matrix ensembles of Floquet Hamiltonians
Here, 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($\overline{E}$) is associated with the Hamiltonian parameter ensemble and the eigenvalue statistics of the Floquet operator. For specific Hamiltonian ensembles, P($\overline{E}$) undergoes a transition which 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 class of generic dynamical processes beyond adiabatic pumps.