  Basic questions on the nature of spin polarization in two terminal systems
and the way in which decoherence breaks Time-Reversal Symmetry (TRS) are
analyzed. We exactly solve several one-dimensional models of tunneling
electrons and show the interplay of spin precession and decay of the
wavefunction in either a U(1) magnetic field or an effective Spin-Orbit (SO)
magnetic field. Spin polarization is clearly identified as the emergence of a
spin component parallel to either magnetic field. We show that Onsager's
reciprocity is fulfilled when time reversal symmetry is present and no spin
polarization arises, no matter the barrier parameters or the SO strength.
Introducing a Buttiker's decoherence probe, that preserves unitarity of time
evolution, we show that breaking of TRS results in a strong spin polarization
for realistic SO, and barrier strengths. We discuss the significance of these
results as a very general scenario for the onset of the Chiral-Induced Spin
Selectivity effect (CISS), now possibly matching experiments in a quantitative
manner.
