Generalized Ginzburg–Landau approach to inhomogeneous phases in nonlocal chiral quark models

Abstract

We analyze the presence of inhomogeneous phases in the QCD phase diagram within the framework of nonlocal chiral quark models. We concentrate in particular in the positions of the tricritical (TCP) and Lifshitz (LP) points, which are studied in a general context using a generalized Ginzburg-Landau approach. We find that for all the phenomenologically acceptable model parametrizations considered the TCP is located at a higher temperature and a lower chemical potential in comparison with the LP. Consequently, these models seem to favor a scenario in which the onset of the first order transition between homogeneous phases is not covered by an inhomogeneous, energetically favored phase.

Meson properties and phase diagrams in a SU(3) nonlocal PNJL model with lattice-QCD-inspired form factors

“…[46] for a review on the subject). In previous works [47,48], we have analyzed the existence of inhomogeneous condensates in the context of nonlocal models by explicitly constructing the associated phase diagrams in the mean-field approximation for a dual chiral density wave [49]. In principle, a full analysis would require to consider general spatial dependent condensates, which turns out to be a very difficult task for an arbitrary three-dimensional configuration.…”

Dynamics of inhomogeneous chiral condensates

“…The Ginzburg-Landau dynamics depends on two fundamental quantities: the energy functional that gives the equilibrium phase diagram and the Onsager coefficient Γ, a time scale related to fluctuation and dissipation processes. We employed NJL-type models to obtain the energy functional; we considered a local NJL model with point-like interactions [4] and a nonlocal NJL model with finite-range interactions [30]. The results are qualitatively similar for both models, but there are interesting differences.…”

“…For the local NJL model, one has [30] α 4b = α 4 , and α 6b /5 = α 6c /3 = 2α 6d ≡ α 6 , which is the case investigated in Ref. [4].…”

“…Following Refs. [4,30], the mean field thermodynamic potential is expanded around the symmetric ground state in powers of the order parameters and their spatial gradients and define it as being the GLW Hamiltonian density…”

Phase transitions in neutron stars and their links to gravitational waves

“…Only at the end of the 90's the possibility of new intermediate phases in the QCD phase diagram, like color superconductivity in which quark Cooper pairs are formed, began to be accepted [31] and later studied in detail in compact stars environments [32]. It has also been suggested that there may be non-homogeneous phases [33][34][35][36], and that there may be a phase of confined quarks with restored chiral symmetry (quarkyonic phase) [37][38][39]. A schematic version of the conjectured phase diagram of QCD is presented in figure 1.…”