Diffusion in disordered systems under iterative measurement

We consider a sequence of idealized measurements of time separation Δt onto a discrete one-dimensional disordered system. A connection with Markov chains is found. For a rapid sequence of measurements, a diffusive regime occurs and the diffusion coefficient D is analytically calculated. In a general point of view, this result suggests the possibility to break the Anderson localization due to decoherence effects. Quantum Zeno effect emerges because the diffusion coefficient D vanishes at the limit Δt^→0.