  We study electron transport in nanojunctions in which an electron on a
quantum dot or a molecule is interacting with an N-state local impurity, a
harmonic ("Holstein") mode, or a two-state system ("spin"). These two models,
the Anderson-Holstein model and the spin-fermion model, can be conveniently
transformed by a shift transformation into a form suitable for a perturbative
expansion in the tunneling matrix element. We explore the current-voltage
characteristics of the two models in the limit of high temperature and weak
electron-metal coupling using a kinetic rate equation formalism, considering
both the case of an equilibrated impurity, and the unequilibrated case.
Specifically, we show that the analog of the Franck-Condon blockade physics is
missing in the spin-fermion model. We complement this study by considering the
low-temperature quantum adiabatic limit of the dissipative spin-fermion model,
with fast tunneling electrons and a slow impurity. While a mean-field analysis
of the Anderson-Holstein model suggests that nonlinear functionalities,
bistability and hysteresis may develop, such effects are missing in the
spin-fermion model at the mean-field level.
