  We develop a Wigner function representation of the quantum transport theory
of the conduction band electrons in Rashba effect resonant tunneling structures
with a phonon bath. In narrow band gap heterostructures, spin splitting occurs
mainly as a result of inversion asymmetry in the spatial dependence of the
potential or as a result of external electric field. This "zero magnetic field
spin splitting" is due to the Rashba term in the effective mass Hamiltonian.
The quantum transport equations are derived using multi-band non-equilibrium
Green's function formulation in generalized Kadanoff-Baym ansatz.
