Let $U_F$ be the Floquet operator of a time periodic hamiltonian $H(t)$. For each positive and discrete observable $A$ (which we call a { \em probe energy}), we derive a formula for the Laplace time average of its expectation value up to time $T$ in terms of its eigenvalues and Green functions at the circle of radius $e^{ 1/T}$. Some simple applications are provided which support its usefulness.
Categories: math-ph math.FA math.MP