Incoherent hydrodynamics of density waves in magnetic fields

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.