Non-perturbative aspects of currents in one-dimensional systems of strongly correlated systems

We study one-dimensional systems of strongly correlated electrons, or quantum wires, at low-energy scales. The Coulomb interactions are fully taken into account by means of non-perturbative techniques such as bosonization, integrability and conformal field theory.; The first setup we consider is a quantum wire with an applied voltage. The characteristic I = I(U) is determined in closed form for any value of the Luttinger constant g; it shows interesting properties such as a bi-stability regime for g and U in a certain range of values and the duality relation between I = I( g, U) and I = I(1/g, U ).; The second setup we consider is a quantum wire suspended between two BCS superconductors. Either superconductors have a gap, whose phase difference χ drives a Josephson current in the quantum wire. We determine I = I(χ) for all values of the Luttinger parameter for this system. The current displays at first an unphysical discontinuity at certain values of χ, which we eliminate by a suitable process of analytic continuation.