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Non-equilibrium steady states of quantum fields on star graphs are explicitlyconstructed. These states are parametrized by the temperature and the chemicalpotential, associated with each edge of the graph. Time reversal invariance isspontaneously broken. We study in this general framework the transportproperties of the Schroedinger and the Dirac systems on a star graph, modelinga quantum wire junction. The interaction, which drives the system away fromequilibrium, is localized in the vertex of the graph. All point-like vertexinteractions, giving rise to self-adjoint Hamiltonians possibly involving theminimal coupling to a static electromagnetic field in the ambient space, areconsidered. In this context we compute the exact electric steady current andthe non-equilibrium charge density. We investigate also the heat transport andderive the Casimir energy density away from equilibrium. The appearance ofFriedel type oscillations of the charge and energy densities along the edges ofthe graph is established. We focus finally on the noise power and discuss thenon-trivial impact of the point-like interactions on the noise.

Non-equilibrium Steady States of Quantum Systems on Star Graphs