  We use holography to derive effective theories of fluctuations in
spontaneously broken phases of systems with finite temperature, chemical
potential, magnetic field and momentum relaxation in which the order parameters
break translations. We analytically construct the hydrodynamic modes
corresponding to the coupled thermoelectric and density wave fluctuations and
all of them turn out to be purely diffusive for our system. Upon introducing
pinning for the density waves, some of these modes acquire not only a gap, but
also a finite resonance due to the magnetic field. Finally, we study the
optical properties and perform numerical checks of our analytical results. A
crucial byproduct of our analysis is the identification of the correct current
which describes the transport of heat in our system.
