Incoherent hydrodynamics of density waves in magnetic fields

TL;DR

This paper uses holography to derive and analyze the diffusive hydrodynamic modes of density waves in systems with magnetic fields, revealing how pinning and magnetic effects influence their behavior and transport properties.

Contribution

It provides the first analytical construction of coupled thermoelectric and density wave modes in such systems, including effects of pinning and magnetic fields, and identifies the correct heat transport current.

Findings

All hydrodynamic modes are purely diffusive in the unpinned case.

Pinning introduces gaps and resonances in some modes due to magnetic fields.

The study clarifies the current responsible for heat transport in these systems.

Abstract

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.