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Particle number violating interactions wash out the primordial asymmetry ofparticle number density generated by some interaction satisfying Sakharovconditions for baryogenesis. In this paper, we study how the primordialasymmetry evolves in time under the presence of particle number violatinginteractions and in the environment of expanding universe. We introduce acomplex scalar model with particle number violating mass terms and calculatethe time evolution of the particle number density with non-equilibrium quantumfield theory. We show how the time evolution of the number density depends onparameters, including the chemical potential related with the particle number,temperature, size of the particle number violating mass terms, and theexpansion rate of the universe. Depending upon whether the chemical potentialis larger or smaller than the rest mass of the scalar particle, behaviors ofthe number density are very different to each other. When the chemicalpotential is smaller than the mass, the interference among the contribution ofoscillators with various momenta reduces the number density in addition to thedilution due to the expansion of universe. In opposite case, the oscillation ofthe particle number density lasts for a long time and the cancellation due tothe interference does not occur.

Time variation of particle and anti-particle asymmetry in an expanding universe