# Holographic Plasmon Relaxation with and without Broken Translations

## TL;DR

This paper investigates the relaxation and dynamics of bulk plasmons in strongly coupled quantum systems using holography, analyzing how various physical parameters and symmetry breaking influence plasmon behavior.

## Contribution

It provides a detailed holographic analysis of plasmon dispersion, damping, and the effects of momentum dissipation and translational symmetry breaking.

## Key findings

- Plasmon dispersion relations depend on electromagnetic coupling, charge, and temperature.
- Momentum dissipation increases damping of plasmon modes.
- Spontaneous symmetry breaking affects the plasma frequency and sound speed.

## Abstract

We study the dynamics and the relaxation of bulk plasmons in strongly coupled and quantum critical systems using the holographic framework. We analyze the dispersion relation of the plasmonic modes in detail for an illustrative class of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we entangle the complicated interplay between the three least damped modes and shed light on the underlying physical processes. Such as the dependence of the plasma frequency and the effective relaxation time in terms of the electromagnetic coupling, the charge and the temperature of the system. Introducing momentum dissipation, we then identify its additional contribution to the damping. Finally, we consider the spontaneous symmetry breaking (SSB) of translational invariance. Upon dialing the strength of the SSB, we observe an increase of the longitudinal sound speed controlled by the elastic moduli and a decrease in the plasma frequency of the gapped plasmon. We comment on the condensed matter interpretation of this mechanism.