Effective Delocalization in the One-Dimensional Anderson Model with Stealthy Disorder

We analyze the 1D Anderson model with stealthy disorder, defined by a power spectrum that vanishes over a continuous band of wave numbers. Perturbative expansion of the self-energy and numerical results show that for small disorder W and prescribed stealthiness χ, the system is effectively delocalized, i.e., the localization length ξ exceeds large system sizes. This unusual behavior follows from the systematic cancellation of leading terms so that ξ scales as W^{-2n} with large n. Since the underlying mechanism depends only on the stealthy disorder, our findings also apply to photonic and phononic waves.