Non-Equilibrium Transport in the Quantum Dot: Quench Dynamics and Non-Equilibrium Steady State

We present an exact method of calculating the non-equilibrium current driven by a voltage drop across a quantum dot. The system is described by the two lead Kondo model with non-interacting Fermi-liquid leads at zero temperature. 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 dot 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 (open system limit). A new type of Bethe Ansatz wavefunction describes the system - it satisfies the Lippmann-Schwinger equation with the two Fermi seas serving as the boundary conditions. We present this wavefunction and give an infinite series expression for the current evaluated in this state to obtain the nonequilibrium steady state current as a function of the voltage. Evaluation of this series is discussed.