SU(6)

Abstract: It is argued that an ultracold quantum degenerate gas of ytterbium 173Yb atoms having nuclear spin I=5/2 exhibits an enlarged SU(6) symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU(n>2) generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU(n) itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU(n>2) ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU(6) Hubbard model.

Abstract: Using several relativistic mean-field models (such as GM1, GM3, NL3, TM1, FSUGold, and IU-FSU) as well as the quark-meson coupling model, we calculate the particle fractions, the equation of state, the maximum mass, and radius of a neutron star within relativistic Hartree approximation. We also discuss in detail the role of nonlinear potentials involved in the mean-field models. In determining the couplings of the isoscalar, vector mesons to the octet baryons, we examine the extension of SU(6) spin-flavor symmetry to SU(3) flavor symmetry. Furthermore, we consider the strange (${\ensuremath{\sigma}}^{*}$ and $\ensuremath{\phi}$) mesons and study how they affect the equation of state. We find that the equation of state in SU(3) symmetry can sustain a neutron star with mass of $(1.8\ensuremath{\sim}2.1){M}_{\ensuremath{\bigodot}}$, even if hyperons exist inside the core. It is noticeable that the strange vector ($\ensuremath{\phi}$) meson and the variation of baryon substructure in matter also play important roles in supporting a massive neutron star.