  We study the localization properties of normal modes in harmonic chains with
mass and spring weak disorder. Using a perturbative approach, an expression for
the localization length is obtained, which is valid for arbitrary correlations
of the disorder, and for practically the whole frequency band. In addition, we
show how to generate effective mobility edges by the use of disorder with long
range self-correlations and cross-correlations. Finally, the transport of
phonons is also analyzed showing effective transparent windows that can be
manipulated through the disorder correlations even for relative short chain
sizes. Our results may have applications in modulating thermal transport,
particularly in the design of thermal filters or in manufacturing
high-thermal-conductivity materials.
