  We introduce a model which may generate particle number asymmetry in an
expanding Universe. The model includes CP violating and particle number
violating interactions. The model consists of a real scalar field and a complex
scalar field. Starting with an initial condition specified by a density matrix,
we show how the asymmetry is created through the interaction and how it evolves
at later time. We compute the asymmetry using non-equilibrium quantum field
theory and as a first test of the model, we study how the asymmetry evolves in
the flat limit.
