  When impurity and phonon scattering coexist, the Boltzmann equation has been
solved accurately for nonlinear electron transport in a quantum wire. Based on
the calculated non-equilibrium distribution of electrons in momentum space, the
scattering effects on both the non-differential (for a fixed dc field) and
differential (for a fixed temperature) mobilities of electrons as functions of
temperature and dc field were demonstrated. The non-differential mobility of
electrons is switched from a linearly increasing function of temperature to a
parabolic-like temperature dependence as the quantum wire is tuned from an
impurity-dominated system to a phonon-dominated one [see T. Fang, {\em et al.},
\prb {\bf 78}, 205403 (2008)]. In addition, a maximum has been obtained in the
dc-field dependence of the differential mobility of electrons. The low-field
differential mobility is dominated by the impurity scattering, whereas the
high-field differential mobility is limited by the phonon scattering [see M.
Hauser, {\em et al.}, Semicond. Sci. Technol. {\bf 9}, 951 (1994)]. Once a
quantum wire is dominated by quasi-elastic scattering, the peak of the
momentum-space distribution function becomes sharpened and both tails of the
equilibrium electron distribution centered at the Fermi edges are raised by the
dc field after a redistribution of the electrons is fulfilled in a symmetric
way in the low-field regime. If a quantum wire is dominated by inelastic
scattering, on the other hand, the peak of the momentum-space distribution
function is unchanged while both shoulders centered at the Fermi edges shift
leftward correspondingly with increasing dc field through an asymmetric
redistribution of the electrons even in low-field regime [see C. Wirner, {\em
et al.}, \prl {\bf 70}, 2609 (1993)].
