  We develop and exploit an out-of-equilibrium theory, valid in arbitrary
dimensions, which does not require initial thermalization. It is perturbative
with respect to a weak time-dependent (TD) Hamiltonian term, but is
non-perturbative with respect to strong coupling to an electromagnetic
environment, or to Coulomb or superconducting correlations. We derive unifying
relations between the current generated by coherent radiation or statistical
mixture of radiations, superimposed on a dc voltage $V_{dc}$, and the
out-of-equilibrium dc current which encodes the effects of interactions. Thus
we extend fully the lateral band-transmission picture, thus quantum
superposition, to coherent many-body correlated states. This provides methods
for a determination of the carrier's charge q free from unknown parameters
through the robustness of the Josephson-like frequency. Similar relations we
have derived for noise have allowed, recently, to determine the fractional
charge in the Fractional Quantum Hall Effect (FQHE) within the Jain series (M.
Kapfer et al, Science 2018). The present theory allows for breakdown of
inversion symmetry and for asymmetric rates for emission and absorption of
radiations. This generates a photo-ratchet effect we exploit to propose a novel
method to measure the charge $q$, as well as spectroscopical analysis of the
out-of-equilibrium dc current and the third cumulant of non-gaussian
statistical radiations. We apply the theory to the Tomonaga-Luttinger Liquid
(TLL), showing a counterintuitive feature: a lorentzian pulse superimposed on
$V_{dc}$ can reduce the current compared to its dc value, at the same $V_{dc}$,
questioning the terminology "photo-assisted". Beyond a charge current, the
theory applies to operators such as spin current in the spin Hall effect, or
voltage drop across a phase-slip Josephson junction.
