Quarkyonic Matter in the Quantum van der Waals Framework: Implications for Neutron Stars

We present a theoretical framework for quarkyonic matter using an excluded-volume model that incorporates the low-density properties of nuclear matter. By introducing attractive mean-field effects and employing a quantum van der Waals approach to nucleons, we reproduce the nuclear liquid-gas transition at sub-saturation densities (n_B ≤ ρ₀) and predict a transition to quarkyonic matter at densities of n_B ≈ 1.5-2 ρ₀, consistent with those observed in intermediate energy heavy-ion collisions. This transition is marked by a characteristic peak in the sound velocity. We extend this formalism to asymmetric nuclear matter, applying it to neutron stars. By modeling the isospin asymmetry with separate Fermi surfaces for u and d quarks, and calibrating the van der Waals interaction parameters using empirical constraints on symmetry energy and neutron star mass-radius relationships, we provide new insights into the role of quarkyonic matter in dense astrophysical environments. Our results offer promising implications for the equation of state in neutron stars, suggesting a significant quarkyonic phase within their cores.