  We derive from first principles, using non-equilibrium field theory, the
quantum Boltzmann equations that describe the dynamics of flavor oscillations,
collisions, and a time-dependent mass matrix in the early universe. Working to
leading non-trivial order in ratios of relevant time scales, we study in detail
a toy model for weak scale baryogenesis: two scalar species that mix through a
slowly varying time-dependent and CP-violating mass matrix, and interact with a
thermal bath. This model clearly illustrates how the CP asymmetry arises
through coherent flavor oscillations in a non-trivial background. We solve the
Boltzmann equations numerically for the density matrices, investigating the
impact of collisions in various regimes.
