Inhomogeneous chiral symmetry breaking in isospin-asymmetric strong-interaction matter

In this thesis we investigate the effects of an isospin asymmetry on inhomogeneous chiral symmetry breaking phases, which are characterized by spatially modulated quark-antiquark condensates. In order to determine the relevance of such phases for the phase diagram of strong-interaction matter, a two-flavor Nambu–Jona-Lasinio model is used to study the properties of the ground state of the system. Confirming the presence of inhomogeneous chiral symmetry breaking in isospin-asymmetric matter for a simple Chiral Density Wave, we generalize the modulation of the quark-antiquark pairs to more complicated shapes and study the effects of different degrees of flavor-mixing on the inhomogeneous phase at non-zero isospin asymmetry. Then, we investigate the occurrence of crystalline chiral symmetry breaking phases in charge-neutral matter, from which we determine the influence of crystalline phases on a quark star by calculating mass-radius sequences. Finally, our model is extended through color-superconducting phases and we study the interplay of these phases with inhomogeneous chiral-symmetry breaking at non-vanishing isospin asymmetry, before we discuss our findings