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The phase diagram of charge and color neutral two-flavor colorsuperconducting quark matter is studied including the homogeneous two-flavorsuperconductor (2SC) and the inhomogeneous Fulde-Ferrell (FF) phases within theNambu-Jona-Lasinio model. The low-temperature domain T < 5 MeV of the phasediagram contains the FF phase, which borders at high temperatures to the 2SCphase. The critical temperature of phase transition from the 2SC to theunpaired state is in the range 20-30 MeV. We derive the equation of state ofmatter and its composition and show that matter in mature compact stars shouldbe in the inhomogeneous FF-like superconducting state. We briefly discuss theastrophysical implications of such a phase in compact stars.

Phase diagram of chiral quark matter: color and electrically neutral Fulde-Ferrell phase