Dark evolution in a time-varying Zeno subspace

We investigate the evolution of a quantum system under the influence of sequential measurements. The measurement scheme distinguishes whether or not the system is in a specified state $| {f_n}>$ at the $n^{\rm th}$ step, where $| {f_n}>$ varies with $n$. Dark evolution corresponds to the situation when all measurements give negative results. We show that dark evolution is unitary in the continuous measurement limit. We derive the effective Hamiltonian, and indicate how $| {f_n}>$ controls quantum state transport.