Weakly nonlinear quantum transport: An exactly solvable model

We have studied the weakly nonlinear quantum transport properties of a two-dimensional quantum wire that can be solved exactly. The nonlinear transport coefficients have been calculated and interesting physical properties revealed. In particular we found that as the incoming electron energy approaches a resonant point given by energy E=Eᵣ, where the transport is characterized by a complete reflection, the second-order nonlinear conductance changes its sign. We have also investigated the establishment of the gauge-invariance condition. We found that for systems with a finite scattering region, correction terms to the theoretical formalism are needed to preserve the gauge invariance. These corrections were derived analytically for this model.