  Quantum particles in a disordered potential, photons or classical waves in a
random medium, or the universe expansion in a fluctuating cosmic field, all
share Anderson localization as a communality. In general, localization is
enhanced for strong disorder and low dimensions. In one dimension and for
discrete uncorrelated random potentials, such as tight binding models, all
states are localized for any disorder strength. This is in contrast to
continuous random potentials, where we show here that regardless of the
strength of the random potential, we have delocalization in the limit where the
roughness length goes to zero. This result was obtained by deriving an
expression for the localization length valid for all disorder strengths. We
solved a non-linear wave equation, whose average over disorder yields the
localization properties of the desired linear wave equation. Our results, not
only explain the origin of the difficulty to observe localization in certain
physical systems, but also show that maximum localization occurs when the
roughness length is comparable to the wavelength, which is relevant to many
experiments in a random medium.
