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We consider the phenomenon of the Andreev reflection of "hadrons" at the interface between hadronic and color superconducting phases, which are expected to appear in the neutron star interior. Here, hadrons are defined as a superposition of constituent quarks, each of which is Andreev-reflected. We study, at the qualitative level, what kind of reflections are possible to come out of incident mesons and baryons in the hadronic phase, attached to different color superconducting phases. Then, some peculiar patterns of the reflections are obtained. [ABSTRACT FROM AUTHOR]

The QCD axial anomaly, by coupling the chiral condensate and BCS pairing fields of quarks in dense matter, leads to a new critical point in the QCD phase diagram [1, 2], which at sufficiently low temperature may terminate the line of phase transitions between chirally broken hadronic matter and color superconducting quark matter. The critical point indicates that matter at low temperature should cross over smoothly from the hadronic to the quark phase, as suggested earlier on the basis of symmetry. We review here the arguments, based on a general Ginzburg-Landau effective Lagrangian, for the existence of the new critical point as well as discuss possible connections between the QCD phase structure and the BEC-BCS crossover in ultracold trapped atomic fermion systems at unitarity and implications for the presence of quark matter in neutron stars. [ABSTRACT FROM AUTHOR]