  The recent study by Bowers and Rajagopal on the possible structures for the
QCD crystalline color superconducting phase favors a cubic structure and allows
for a first discussion of the QCD dynamics in the crystalline phase. The cubic
structure leads to complete breaking of traslation invariance and to three
phonon modes. We discuss the expected form of the effective Lagrangian and the
phonon dispersion laws assuming the proposed crystal structure. Besides the
interest for QCD and the related possible relevance to compact stars these
considerations may become useful to atomic systems exhibiting crystalline
superfluidity.
