  The influence of the electrons interaction with longitudinal acoustic phonons
on magnetoeletric and spin-related transport effects are investigated. The
physical system under consideration has been assumed to be a two dimensional
electron gas system with both Rashba and Dreesselhaus spin-orbit couplings. In
the works which have been previously performed in this field it has been shown
that in the non-equilibrium regime, the Rashba and Dreesselhaus couplings can
not be responsible for spin-current where in the absence of other interactions
such as lattice vibrations identically vanishes. In the current work we have
employed a semi-classical method by using the Boltzmann approach. It was shown
that the spin-current of the system, in general, does not go all the way to
zero at any value of the spin-orbit couplings. It was also shown that the spin
accumulation of the system can be influenced by the electron-phonon coupling.
