  The Schr\"odinger-Poisson-Newton equations for crystals with a cubic lattice
and one ion per cell are considered. The ion charge density is assumed i) to
satisfy the Wiener and Jellium conditions introduced in our previous paper
[28], and ii) to be exponentially decaying at infinity. The corresponding
examples are given. We study the linearized dynamics at the ground state. The
dispersion relations are introduced via spectral resolution for the
non-selfadjoint Hamilton generator using the positivity of the energy
established in [28]. Our main result is the dispersion decay in the weighted
Sobolev norms for solutions with initial states from the space of continuous
spectrum of the Hamilton generator. We also prove the absence of singular
spectrum and limiting absorption principle. The multiplicity of every
eigenvalue is shown to be infinite. The proofs rely on novel exact bounds and
compactness for the inversion of the Bloch generators and on uniform
asymptotics for the dispersion relations. We derive the bounds by the energy
positivity from [28]. We also use the theory of analytic sets.
