An exact solution of the Dirac equation with CP violation
  We consider Yukawa theory in which the fermion mass is induced by a Higgs
like scalar. In our model the fermion mass exhibits a temporal dependence,
which naturally occurs in the early Universe setting. Assuming that the complex
fermion mass changes as a tanh-kink, we construct an exact, helicity
conserving, CP-violating solution for the positive and negative frequency
fermionic mode functions, which is valid both in the case of weak and strong CP
violation. Using this solution we then study the fermionic currents both in the
initial vacuum and finite density/temperature setting. Our result shows that,
due to a potentially large state squeezing, fermionic currents can exhibit a
large oscillatory magnification. Having in mind applications to electroweak
baryogenesis, we then compare our exact results with those obtained in a
gradient approximation. Even though the gradient approximation does not capture
the oscillatory effects of squeezing, it describes quite well the averaged
current, obtained by performing a mode sum. Our main conclusion is: while the
agreement with the semiclassical force is quite good in the thick wall regime,
the difference is sufficiently significant to motivate a more detailed
quantitative study of baryogenesis sources in the thin wall regime in more
realistic settings.
