  Recently we showed how a non-local Nambu-Jona-Lasinio model comes out from
QCD in the low-energy limit. In this way, it is possible to fix all the free
parameters of the model with physical ones. We use this approach to derive a
local limit to the Nambu-Jona-Lasinio model with the parameters those obtained
from QCD in order to fix the physical parameters of $\rho$ condensation. $\rho$
condensation is a consequence of the highly non-trivial behavior of the QCD
vacuum in presence a very strong magnetic field giving rising to
superconductive behavior in quark matter. Determination of the proper
parameters for this state can be an important helpful guide to identify it
experimentally.
