Flow-equation approach to quantum systems driven by an amplitude-modulated time-periodic force

We apply the method of flow equations to describe quantum systems subject a time-periodic drive with time-dependent envelope. The driven Hamiltonian is expressed in terms its constituent Fourier harmonics amplitudes that may vary as function time. time evolution system described phase-independent effective and complementary micromotion operator are generated by deriving solving equations. These implement respect an auxiliary variable facilitate gradual transformation quasienergy matrix (the Kamiltonian) into block diagonal form extended space. construct generator prevents appearance additional during flow, thus enabling implementation computer algebra system. Automated generation otherwise cumbersome high-frequency expansions (for both micromotion) arbitrary order becomes straightforward for Hamiltonians expressible finite Hermitian operators. give several specific examples discuss possibility extend treatment cover rapid modulation