The phase space structure of zero temperature Quarkyonic matter is a Fermi sphere of Quark Matter, surrounded by a shell of Nucleonic matter. We construct a quasi particle model of Quarkyonic Matter based on the constituent quark model, where the quark and nucleon masses are related by mQ = mN /Nc, and Nc is the number of quark colors. The region of occupied states is for quarks kQ < kF /Nc, and for nucleons kF < kN < kF + ∆. We first consider the general problem of Quarkyonic Matter with hard core nucleon interactions. We then specialize to a quasi-particle model where the hard core nucleon interactions are accounted for by an excluded volume. In this model, we show that the nucleonic shell forms past some critical density related to the hard core size, and for large densities becomes a thin shell. We explore the basic features of such a model, and argue this model has the semi-quantitative behaviour needed to describe neutron stars.

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We calculate the nucleon self-energies in isospin-asymmetric nuclear matter using QCD sum rules. Taking the difference of these for the neutron and proton enables us to express the potential part of the nuclear symmetry energy in terms of local operators. We find that the scalar (vector) self energy part gives a negative (positive) contribution to the nuclear symmetry energy which is consistent with the results from relativistic mean field theories. Moreover, we find that an important contribution to the negative contribution of the scalar self energy comes from the twist-4 matrix elements, whose leading density dependence can be extracted from deep inelastic scattering experiments. This suggests that the twist-4 contribution partly mimics the exchange of the δ meson and that it constitutes an essential part in the origin of the nuclear symmetry energy from QCD. Our result also extends an early success of QCD sum rule method in understanding the symmetric nuclear matter in terms of QCD variables to the asymmetric nuclear matter case.

The nuclear density dependencies of the neutron and Σ and Λ hyperons are important inputs in the determination of the neutron star mass as the appearance of hyperons coming from strong attractions significantly changes the stiffness of the equation of state (EOS) at iso-spin asymmetric dense nuclear matter. In-medium spectral sum rules have been analyzed for the nucleon, Σ, and Λ hyperon to investigate their properties up to slightly above the saturation nuclear matter density by using the linear density approximation for the condensates. The construction scheme of the interpolating fields without derivatives has been reviewed and used to construct a general interpolating field for each baryon with parameters specifying the strength of independent interpolating fields. Optimal choices for the interpolating fields were obtained by requiring the sum rules to be stable against variations of the parameters and the result to be consistent with known phenomenology. The optimized result shows that Ioffe's choice is not suitable for the Λ hyperon sum rules. It is found that, for the Λ hyperon interpolating field, the up and down quark combined into the scalar diquark structure u T Cγ5d should be emphasized to ensure stable sum rules. The quasi-Σ and -Λ hyperon energies are always found to be higher than the quasineutron energy in the region 0.5 < ρ/ρ0 < 1.5 where the linear density approximation in the sum-rule analysis is expected to be reliable.