Interaction-free evolution in the presence of time-dependent Hamiltonians

The generalization of the concept of interaction-free evolutions (IFE) [Napoli et al., Phys. Rev. A 89, 062104 (2014)] to the case of time-dependent Hamiltonians is discussed. It turns out that the time-dependent case allows for much richer structures of interaction-free states and interaction-free subspaces. The general condition for the occurrence of IFE is found and exploited to analyze specific situations. Several examples are presented, each one associated to a class of Hamiltonians with specific features.