Pion condensation in the Gross-Neveu model with nonzero baryon and isospin chemical potentials

The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional spacetime are investigated in the presence of the isospin $\mu_I$ as well as quark number $\mu$ chemical potentials both at zero and nonzero temperatures. The consideration is performed in the limit $N_c\to\infty$, i.e. in the case with an infinite number of colored quarks. In the plane of parameters $\mu_I,\mu$ a rather rich phase structure is found, which contains phases with and without pion condensation. Moreover, we have found a great variety of one-quark excitations of these phases, including gapless and gapped quasiparticles.