Dynamics of one-site fermionic model in the presence of precessing magnetic field

The one site self-interacting fermionic model is considered in the presence of an external magnetic field precessing with constant angular velocity around a fixed axis. We get the exact density operator for the identical particle system as well as its one-particle properties, for general initial conditions. Due to the non-trivial topology of the external magnetic field, the one-particle states get Berry's phases. We show that the geometric phases contribute to the frequency of the one-particle population state in the adiabatic regime.