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We discuss the dynamics of particles in one dimension in potentials that are random both in space and in time. The results are applied to recent optics experiments on Anderson localization, in which the transverse spreading of a beam is suppressed by random fluctuations in the refractive index. If the refractive index fluctuates along the direction of the paraxial propagation of the beam, the localization is destroyed. We analyze this broken localization, in terms of the spectral decompositiondoi:10.1088/1367-2630/14/4/043047 fatcat:blbv7644tbe73iu2hmogz6e7xi