  A new mechanism for generating particle number asymmetry (PNA) has been
developed. This mechanism is realized with a Lagrangian including a complex
scalar field and a neutral scalar field. The complex scalar carries U(1) charge
which is associated with the PNA. It is written in terms of the condensation
and Green's function, which is obtained with two-particle irreducible (2PI)
closed time path (CTP) effective action (EA). In the spatially flat universe
with a time-dependent scale factor, the time evolution of the PNA is computed.
We start with an initial condition where only the condensation of the neutral
scalar is non-zero. The initial condition for the fields is specified by a
density operator parameterized by the temperature of the universe. With the
above initial conditions, the PNA vanishes at the initial time and later it is
generated through the interaction between the complex scalar and the
condensation of the neutral scalar. We investigate the case that both the
interaction and the expansion rate of the universe are small and include their
effects up to the first order of the perturbation. The expanding universe
causes the effects of the dilution of the PNA, freezing interaction and the
redshift of the particle energy. As for the time dependence of the PNA, we
found that PNA oscillates at the early time and it begins to dump at the later
time. The period and the amplitude of the oscillation depend on the mass
spectrum of the model, the temperature and the expansion rate of the universe.
