Quantum effects after decoherence in a quenched phase transition

We study a quantum mechanical toy model that mimics some features of a quenched phase transition. Both by virtue of a time-dependent Hamiltonian or by changing the temperature of the bath we are able to show that even after classicalization has been reached. the system may display quantum behavior again. We explain this behavior in terms of simple nonlinear analysis and estimate relevant time scales that match the results of numerical simulations of the master equation. This opens new possibilities both in the study of quantum effects in nonequilibrium phase transitions and in general time-dependent problems where quantum effects may be relevant even after decoherence has been completed.