# Spatially modulated chiral condensates

## TL;DR

This paper explores properties of spatially varying chiral condensates in dense quark matter, comparing different ansatz solutions and analyzing their free energies, dispersion relations, and Fourier characteristics.

## Contribution

It introduces a formalism for inhomogeneous chiral condensates and compares plane-wave, sinusoidal, and kink crystal solutions in dense quark matter.

## Key findings

- Sinusoidal and plane-wave solutions have distinct free energies and dispersion relations.
- The real kink crystal can be related to sinusoidal solutions via Fourier analysis.
- Different modulations exhibit unique properties relevant to dense quark matter phases.

## Abstract

I discuss some properties of spatially dependent chiral condensates, focusing on one-dimensional modulations. After briefly introducing a generic formalism for studying inhomogeneous solutions in dense quark matter, I consider a plane-wave and a sinusoidal ansatz, and discuss the relationship between their order parameters and free energies, as well as a comparison of their dispersion relations. I then introduce a real kink crystal, and discuss its relationship with the sinusoidal ansatz by performing a Fourier analysis of this kind of solution.