# Incoherent hydrodynamics and density waves

## TL;DR

This paper develops an effective incoherent hydrodynamics framework for holographic lattice phases at finite chemical potential, including phases with spontaneously broken internal symmetries, revealing coupled diffusive modes.

## Contribution

It introduces a new effective theory for incoherent hydrodynamics in holographic phases with broken symmetries, extending previous models to include coupled diffusive modes.

## Key findings

- Normal phase exhibits two diffusive charge density modes.
- Broken phase features an additional coupled hydrodynamic degree of freedom.
- Effective theory accurately describes long-wavelength excitations in both phases.

## Abstract

We consider thermal phases of holographic lattices at finite chemical potential in which a continuous internal bulk symmetry can be spontaneously broken. In the normal phase, translational symmetry is explicitly broken by the lattice and the only conserved quantities are related to time translations and the electric charge. The long wavelength excitations of the corresponding charge densities are described by incoherent hydrodynamics yielding two perturbative modes which are diffusive. In the broken phase an additional hydrodynamic degree of freedom couples to the local chemical potential and temperature and we write an effective theory describing the coupled system at leading order in a derivative expansion.