The Inhomogeneous Road to Chiral Symmetry Breaking: A Ginzburg–Landau–Langevin Analysis

We investigate the time evolution of the quark condensate toward a chiral symmetry broken phase in hot and dense quark matter using a field-theoretic quark model with nonlocal chiral-invariant four-fermion coupling. By purposely selecting a parameter set in which inhomogeneous phases are energetically disfavored, we nonetheless observe the emergence of metastable patterned configurations that appear to persist for remarkably long timescales. These findings suggest that even when not fully stable, inhomogeneous phases may play a significant role in the dynamics of chiral symmetry breaking and restoration. To gain deeper insight into these phenomena, we also analyze the impact of the dimensionality of coordinate space on both the formation and stability of inhomogeneous chiral condensates.