Quantum impurity models can be very naturally driven out-of-equilibrium, by connecting them to several baths in different equilibrium states. The description of the steady state resulting from biasing the baths is still an open problem in the generic case where interactions are present. In the case of integrable impurity models, it turns out that the exact solution *in equilibrium* cannot be straightforwardly extended to describe the out-of-equilibrium properties. In this talk, I will show that in some integrable impurity models, their exists a method allowing for an exact and systematic expansion in the bias, in principle at arbitrary order. This method will be applied to the specific example of the interacting resonant level model, where electrical and thermal currents can be computed.

Lab. Matériaux et Phénomènes Quantiques, Univ. Paris Diderot