  The present letter finds the complete set of exact solutions of the
time-dependent generalized Cini model by making use of the Lewis-Riesenfeld
invariant theory and the invariant-related unitary transformation formulation
and, based on this, the general explicit expression for the decoherence factor
is therefore obtained. This study provides us with a useful method to consider
the geometric phase and topological properties in the time-dependent quantum
decoherence process.
