Abstract: I discuss possible features of the phase diagram for Quantum ChromoDynamics in the plane of temperature, T, and net quark
chemical potential, mu, at moderate T and nonzero mu. This includes the appearance of Quantum Pion Liquids, which disorder
any spatially inhomogeneous state (such as a pion condensate), and a "moat" regime, where pions get lighter as they move faster
(as least for some momentum). I then discuss how one might study this in a toy model in 1+1 dimensions, QZD, which is
a Z(3) gauge theory coupled to three degenerate flavors of massive fermions.