Inhomogeneous charged pion condensation phenomenon in the NJL$_2$ model with quark number and isospin chemical potentials

TL;DR

This paper explores how inhomogeneous charged pion condensation occurs in a (1+1)-dimensional NJL model with chemical potentials, revealing spatially inhomogeneous phases in dense asymmetric quark matter.

Contribution

It demonstrates that charged pion condensation in the NJL$_2$ model is spatially inhomogeneous rather than homogeneous under certain conditions.

Findings

Charged pion condensation is spatially inhomogeneous in the model.

Inhomogeneous phases are favored in dense, asymmetric quark matter.

The large-$N_c$ limit simplifies the analysis of these phenomena.

Abstract

The properties of two-flavored massive Nambu--Jona-Lasinio model in (1+1)-dimensional spacetime are investigated in the presence of isospin and quark number chemical potentials. The consideration is performed in the large-$N_c$ limit, where $N_c$ is the number of colored quarks. It is shown in the framework of this model that charged pion condensation phenomenon of dense quark/hadron isotopically asymmetric matter is rather a spatially inhomogeneous than a homogeneous one.