Non uniform structures of the nucleon matter at subnuclear densities are numerically studied by means of the density functional theory with relativistic mean-fields coupled with the electric field. A particular role of the charge screening effects is demonstrated.

A density wave in quark matter is discussed at finite temperature, which occurs along with the chiral condensation, and is described by a dual standing wave in scalar and pseudo-scalar condensates on the chiral circle. The mechanism is quite similar to that for the spin density wave suggested by Overhauser, and entirely reflects many-body effects. It is found within a mean-field approximation for NJL model that the chiral condensed phase with the density wave develops at a high-density region just outside the usual chiral-transition line in phase diagram. A magnetic property of the density wave is also elucidated.

Usually it is believed that the Hartree-Fock state of quark matter is a Fermi gas state with no polarisation of spins. We examine the possibility of the polarised quark liquid interacting with the one-gluon-exchange interaction.It is suggested that the Hartree-Fock state shows a spontaneous magnetic instability at low densities through the same mechanism as the appearance of ferromagnetism in electron gas. Metastability of the polarised quark liquid is also discussed.

We analyze the different possibilities for the hadron-quark phase transition occurring in beta-stable matter including hyperons in neutron stars. We use a Brueckner-Hartree-Fock approach including hyperons for the hadronic equation of state and a generalized MIT bag model for the quark part. We then point out in detail the differences between Maxwell and Gibbs phase transition constructions including the effects of surface tension and electromagnetic screening. We find only a small influence on the maximum neutron star mass, whereas the radius of the star and in particular its internal structure are more affected.

The possibility of structured mixed phases at first order phase transitions in neutron stars is re-examined by taking into account charge screening and surface effects. The transition from the hadron npe phase to the quark phase is studied. Two possibilities, the mixed phase and two separate phases given by the double-tangent (Maxwell) construction are considered. Inhomogeneous profiles of the electric potential and their contribution to the energy are analytically calculated. The electric field configurations determine the droplet size and the geometry of structures.

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We calculate stellar oscillations including the hadron-quark mixed phase considering the finite size effects. We find that it is possible to distinguish whether the density discontinuity exists or not in the stars, even if one will observe the gravitational waves of the fundamental mode. Additionally, the normalized eigenfrequencies of pressure modes depend strongly on the stellar mass and on the adopted equation of state. Especially, in spite of the fact that the radius of the neutron star with $1.4M_\odot$, which is standard mass, is almost independent from the equation of state with quark matter, the frequencies of pressure modes depend on the adopted equation of state. Thus, via observing the many kinds of gravitational waves, it will be possible to make a restriction on the equation of state.Comment: accepted for publication in Physical Review

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