Inhomogeneous phases of strongly interacting matter

We discuss possible inhomogeneous phases in two regions of the QCD phase diagram: We begin with color superconducting quark matter at moderately high densities, which is an imbalanced Fermi system due to the finite strange quark mass and neutrality constraints. Within an NJL-type toy model we find that this situation could lead to the formation of a soliton lattice. Similar solutions also exist in the context of the chiral phase transition. As an interesting result, the first-order transition line in the phase diagram of homogeneous phases gets replaced by an inhomogeneous phase which is bordered by two second-order transition lines.