Energy transfer in random-matrix ensembles of Floquet Hamiltonians

Abstract

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(E̅) is associated with the Hamiltonian parameter ensemble and the eigenvalue statistics of the Floquet operator. For specific Hamiltonian ensembles, P(E̅) 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.

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