Non-Equilibrium Transport in the Kondo Model: Strong and Weak Coupling

We present an exact method of calculating the non-equilibrium current driven by a voltage drop across a quantum impurity. The system is described by the two lead Kondo model with non-interacting Fermi-liquid leads. We prepare the system in an initial state consisting of a free Fermi sea in each lead with the voltage drop given as the difference between the two Fermi levels. We quench the system by coupling the impurity to the leads at t=0 and following the time evolution of the wavefunction. In the long time limit, a steady state emerges provided that the size of the system is large compared to the time of evolution (the open system limit). We determine the wavefunction explicitly at any time and show, in particular, that the long time limit satisfies the Lippmann-Schwinger equation with the two Fermi seas serving as the boundary conditions. Using this wavefunction, we obtain an infinite series expression for the current as a function of voltage, either in powers of the antiferromagnetic Kondo coupling constant J or in powers of 1/J. Evaluating the first few terms, we find that a quench to small J reproduces known results while a quench to large J leads to a pre-thermalized regime of maximal conductance with ferromagnetic corrections.