A microscopic study of pion condensation within Nambu--Jona-Lasinio model

We have studied the phenomenology of pion condensation in 2-flavor neutral quark matter at finite density with Nambu--Jona-Lasinio (NJL) model of QCD. We have discussed the role of the bare quark mass $m$ and the electric chemical potential $\mu_{e}$ in controlling the condensation. The central result of this work is that the onset for $\pi$-condensed phase occurs when $|\mu_{e}|$ reaches the value of the in-medium pion mass $M_{\pi}$ provided the transition is of the second order, even for a composite pion system in the medium. Finally, we have shown that the condensation is extremely fragile with respect to the explicit chiral symmetry breaking via a finite current quark mass.