  We present a construction of non-equilibrium steady states in one-dimensional
quantum critical systems carrying energy and charge fluxes. This construction
is based on a scattering approach within a real-time hamiltonian reservoir
formulation. Using conformal field theory techniques, we prove convergence
towards steady states at large time. We discuss in which circumstances these
states describe the universal non-equilibrium regime at low temperatures. We
compute the exact large deviation functions for both energy and charge
transfers, which encode for the quantum and statistical fluctuations of these
transfers at large time. They are universal, depending only on fundamental
constants (h, k_B), on the central charge and on the external parameters such
as the temperatures or the chemical potentials, and they satisfy fluctuation
relations. A key point consists in relating the derivatives of these functions
to the linear response functions but at complex shifted external parameters.
