Adiabatic approximation standard techniques

Combining the KAM techniques with the RWT will allow us to construct effective Hamiltonians in a systematic way and to estimate the order of the neglected terms (see Section III.D). We show that the KAM technique allows us to partition at a desired order operators in orthogonal Hilbert subspaces. We adapt this partitioning technique to treat Floquet Hamiltonians. Its connection with the standard adiabatic elimination is shown at a second-order approximation. 

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