Chiral symmetry and density waves in quark matter

A density wave in quark matter is discussed at finite temperature, which occurs along with the chiral condensation, and is described by a dual standing wave in scalar and pseudoscalar condensates on the chiral circle. The mechanism is quite similar to that for the spin density wave suggested by Overhauser and entirely reflects many-body effects. It is found within a mean-field approximation for the Nambu-Jona-Lasinio model that the chiral-condensed phase with the density wave develops at a high-density region just outside the usual chiral-transition line in phase diagram. A magnetic property of the density wave is also elucidated.