Short-Time Behavior of a System Ruled by Non-Hermitian Time-Dependent Hamiltonians

The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second-order perturbative approach. The resulting expression allows for the analysis of some situations which could be of interest in the field of quantum technology. For example, it becomes possible to predict a quantum Zeno effect even in the presence of decay processes.