  We apply the recently proposed quasi-classical approach for a second
quantized many-electron Hamiltonian in Cartesian coordinates [J. Chem. Phys.
137, 154107 (2012)] to correlated nonequilibrium quantum transport. The
approach provides accurate results for the resonant level model for a wide
range of temperatures, bias and gate voltages, correcting for the flaws of our
recently proposed mapping using action-angle variables. When electron-electron
interactions are included, higher order schemes are required to map the
two-electron integrals, leading to semi-quantitative results for the Anderson
impurity model. In particular, we show that the current mapping is capable of
capturing qualitatively the Coulomb blockade effect.
