Floquet Hamiltonian

A Floquet Hamiltonian generates the evolution over one period of a time-periodic Quantum Hamiltonian. For period $T$, choose $H_F$ such that $U(T,0)=e^{-i{H}_{F}T/\hslash }$. Its eigenvalues are quasienergies, defined modulo $\hslash \omega$ with $\omega =2\pi /T$.

Taking a logarithm of the same unitary permits different branches, so the quasienergy convention must be specified. A complete description within the period also needs the periodic micromotion; the stroboscopic generator alone does not determine every intermediate observable. At sufficiently high drive frequency, an inverse-frequency expansion can approximate $H_F$, but resonances or long-time heating can limit its validity. The construction is useful for separating repeated-cycle dynamics from motion within a cycle.