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In this paper, we present a general correspondence between the mosaic andnon-mosaic models, which can be used to obtain the exact solution for themosaic ones. This relation holds not only for the quasicrystal models, but alsofor the Anderson models. Despite the different localization properties of thespecific models, this relationship shares a unified form. Applying our methodto the mosaic Anderson models, we find that there is a discrete set of extendedstates. At last, we also give the general analytical mobility edge for themosaic slowly varying potential models and the mosaic Ganeshan-Pixley-Das Sarmamodels.

A general approach to the exact localized transition points of 1D mosaic disorder models