2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90884The 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.5 pages, LatexQuantum Physicstext