  This work relates quantitatively homogenization to Anderson localization for
acoustic operators in disordered media. By blending dispersive estimates for
homogenized operators and quantitative homogenization of the wave equation, we
derive large-scale dispersive estimates for waves in disordered media that we
apply to the spreading of low-energy eigenstates. This gives a short and direct
proof that the lower spectrum of the acoustic operator is purely absolutely
continuous in case of periodic media, and it further provides new lower bounds
on {the localization length} of possible eigenstates in case of quasiperiodic
or random media.
