Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu–Jona-Lasinio model

We study the dynamics of inhomogeneous scalar and pseudoscalar chiral order parameters within the framework of the time-dependent Ginzburg-Landau equations. We utilize a nonlocal chiral quark model to obtain the phase diagram of the model as a function of temperature and baryon chemical potential and study the formation of metastable spatial domains of matter where the order parameters acquire a spatial modulation in the course of their dynamical evolution. We found that, before reaching the expected equilibrium homogeneous state, both scalar and pseudoscalar chiral condensates go through long-lived metastable inhomogeneous structures. For different initial configurations of the order parameters, the lifetimes of the inhomogeneous structures are compared to timescales in a relativistic heavy-ion collision.

Figure 1

Normalized GL coefficients as a function of temperature, for values of $\mu$ varying between $\mu =0$ and 300 MeV, enclosed by the solid and dashed lines, respectively.

Figure 2

Top panel: average of $\sigma (x,\tau )$ over the volume, Eq. (14). Lower panels: snapshots of $\sigma (x,\tau )$ at different values of $\tau$ and $\mu$. The initial configuration is a Gaussian profile (light-grey dotted line).

Figure 3

Top panel: average of $\sigma (x,\tau )$ over the volume. Bottom panel: snapshots of $\sigma (x,\tau )$ at different values of $\tau$. The initial configuration is a dual chiral density wave superimposed with Gaussian noise (light-grey dotted line).

Figure 4

TDGL evolution for the pseudoscalar field for a DCDW initial profile superimposed with Gaussian noise (light-grey dotted line).

Figure 5

Formation of inhomogeneous configurations for an antisymmetric random initial profile (light-gray dashed lines). When ${\mathrm{\Gamma }}_{\pi }=0$, the equilibrium state is an isolated soliton configuration (bottom panel). When the order parameters are coupled, metastable intermediate profiles are formed before reaching a homogeneous configuration at equilibrium (top panel).