Low-temperature conductance and DC current noise in a quantum wire with impurity

The nonlinear conductance for tunneling through an impurity in a Luttinger liquid and the nonequilibrium DC current noise are calculated exactly for low temperatures. We present a pedestrian pathway towards the exact solution which is based on analytic properties and on a duality between weak and strong backscattering. The prefactor of the T^2 enhancement is shown to be universally expressed in terms of zero temperature properties.