 Floquet operator

For a periodic Hamiltonian $H(t+T)=H(t)$, the Floquet operator is the unitary operator evolving a quantum state through one complete period, at a fixed starting phase of the drive. The composition law gives $U(NT,0)=U_F^N$. Choosing a different starting phase conjugates $U_F$ by a unitary operator, so its eigenvalues are unchanged.