We study the phase structure of the two-flavor Nambu–Jona-Lasinio (NJL) model in the chiral limit, extending a previous study of the competition of an inhomogeneous chiral phase and a two-flavor color-superconducting (2SC) phase [M. Sadzikowski, Phys. Lett. B 553, 45 (2003); M. Sadzikowski, Phys. Lett. B 642, 238 (2006)]. There, an analytic expression for the dispersion relations for quasiparticle excitations in the presence of both a particular inhomogeneous chiral condensate, the so-called chiral density wave (CDW), and a homogeneous 2SC condensate was found. In this work we show how to determine the dispersion relations for arbitrary modulations of the chiral condensate in the presence of a homogeneous 2SC condensate, if the dispersion relations in the absence of color superconductivity are known. In our calculations, we employ two different Ansätze for the inhomogeneous chiral condensate, the CDW as well as the real-kink crystal (RKC). Depending on the value of the diquark coupling we find a region of the phase diagram where the inhomogeneous chiral and the 2SC condensates coexist, confirming results of M. Sadzikowski [Phys. Lett. B 553, 45 (2003); 642, 238 (2006)]. Decreasing the diquark coupling favors the inhomogeneous phase over the coexistence phase. On the other hand, increasing the diquark coupling leads to a larger 2SC phase, while the inhomogeneous chiral and the coexistence phases become smaller. In agreement with previous studies the RKC Ansatz is energetically preferred over the CDW Ansatz. Both Ansätze lead to a qualitatively similar phase diagram, however, the coexistence phase is smaller for the RKC Ansatz.

中文翻译：

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NJL模型中不均匀手性相和两种风味颜色超导的竞争

我们在手性极限条件下研究了两种风味的Nambu–Jona-Lasinio（NJL）模型的相结构，扩展了先前对不均匀手性相和两种风味的颜色超导（2SC）相竞争的研究[M 。Sadzikowski，物理学。来吧 B 553，45（2003）; M. Sadzikowski，物理学。来吧 乙 642，238（2006）]。在那里，在存在特定的不均匀手性冷凝物，所谓的手性密度波（CDW）和均匀的2SC冷凝物的情况下，找到了准粒子激发的色散关系的解析表达式。在这项工作中，我们将说明如果已知在不存在颜色超导的情况下的色散关系，则如何确定在均相2SC冷凝物存在下手性冷凝物的任意调制的色散关系。在我们的计算中，我们使用了两种不同的Ansätze对于不均匀的手性冷凝物，CDW以及实扭结晶体（RKC）。根据Diquark耦合的值，我们找到了相图中不均匀的手性和2SC冷凝物共存的区域，这证实了M. Sadzikowski的结果。来吧 B 553，45（2003）;642，238（2006）]。降低双夸克偶联有利于不均匀相优于共存相。另一方面，增加双夸克偶联导致较大的2SC相，而不均匀的手性相和共存相则较小。与先前的研究一致，RKC Ansatz在能量上优于CDW Ansatz。两种Ansätze都得出定性相似的相图，但是RKC Ansatz的共存相较小。