  We investigate pion superfluidity and its effect on meson properties and
equation of state at finite temperature and isospin and baryon densities in the
frame of standard flavor SU(2) NJL model. In mean field approximation to quarks
and random phase approximation to mesons, the critical isospin chemical
potential for pion superfluidity is exactly the pion mass in the vacuum, and
corresponding to the isospin symmetry spontaneous breaking, there is in the
pion superfluidity phase a Goldstone mode which is the linear combination of
the normal sigma and charged pion modes. We calculate numerically the gap
equations for the chiral and pion condensates, the phase diagrams, the meson
spectra, and the equation of state, and compare them with that obtained in
other effective models. The competitions between pion superfluidity and color
superconductivity at finite baryon density and between pion and kaon
superfluidity at finite strangeness density in flavor SU(3) NJL model are
briefly discussed.
