The Coulomb interaction effect and the surface effect are consistently taken into account in the hadron-quark mixed phase. These two finite-size effects greatly change the properties of the mixed phase and restrict its density region. In particular, the charge screening effect and the rearrangement of the charged particles are elucidated. Keeping the Gibbs conditions throughout the numerical procedure, we show the Maxwell construction effectively regain the physical meaning and the equation of state becomes similar to that given by the Maxwell construction.

Non-uniform structures of mixed phases at the first-order phase transition to charged kaon condensation are studied using a density functional theory within the relativistic mean field model. Including electric field effects and applying the Gibbs conditions in a proper way, we numerically determine density profiles of nucleons, electrons and condensed kaons. Importance of charge screening effects is elucidated and thereby we show that the Maxwell construction is effectively justified. Surface effect is also studied to figure out its effect on the density profiles.

Hadron-quark mixed phase is expected in a wide region of the inner structure of hybrid stars. However, we show that the hadron-quark mixed phase should be restricted to a narrower region to because of the charge screening effect. The narrow region of the mixed phase seems to explain physical phenomena of neutron stars such as the strong magnetic field and glitch phenomena, and it would give a new cooling curve for the neutron star. PACS numbers: Valid PACS appear hereIt is widely believed that there should be quark matter in the inner core region of neutron stars because the central density of neutron stars is sufficiently high for nucleons to dissolve into more elementary particles, namely quarks. Nowadays we consider that compact stars consist of not only nuclear matter but also other matter such as hyperons and quarks. We call such stars hybrid stars.Although deconfinement phase transition is still not clearly understood, many authors have studied the transition through modeling and first-principle calculations such as those of lattice QCD. Properties of quark matter have been actively studied theoretically in terms of quark-gluon plasma, color superconductivity [1, 2] and magnetism [3][4][5], and experimentally in terms of relativistic heavy-ion collisions [6] and early-universe and compact stars [7,8]. Such studies are continuing to provide exciting results [9].Because many theoretical calculations have suggested that deconfinement transition is of first order at low temperature and high density [10,11], we assume it to be a first-order phase transition here. The Gibbs condition (GC) [12] then gives rise to various structured mixed phases (SMPs). The SMPs suggested by Heiselberg et al. [13] and Glenndening and Pei [14] suggest a crystalline structure of the mixed phase in the core region of hybrid stars. Such structures are called "droplets", "rods", "slabs", "tubes", and "bubbles". These SMPs exist within a wide density range if we take a moderate value of the surface tension. However, if the surface effect is strong, the SMPs are limited to a narrow density region. On the other hand, Voskresensky et al. [15] reported the charge screening effect for several cases of droplets and slabs. They showed that even if we take a moderate value of the surface tension, SMPs cannot exist because of the charge screening effect. They referred to this phenomenon as mechanical instability. However, they used a linear approximation to solve the Poisson equation.We have presented the equation of state (EOS) for the mixed phase taking into account the charge screening effect [16] without recourse to any approximation. The * endo@t.kagawa-nct.ac.jp EOS is similar to that obtained from the Maxwell construction (MC). The allowed region of the mixed phase should then be narrow due to the charge screening effect.Recently "black stars" have been proposed by Barcelo et al. [17], who suggested that quantum effects prevent a star from collapsing into a "Black hall". Therefore, the EOS of hadron matter in the high-density states plays...

The Coulomb screening effect and the finite-size effect such as surface tension are figured out in the hadron-quark deconfinement phase transition. We study the mixed phase of the quark droplets immersed in hadron matter. We see that the droplet phase is mechanically unstable if the surface tension is strong enough. Once the Coulomb potential is properly taken into account, we could effectively satisfy the condition for charge chemical equilibrium in the Maxwell construction. As a result, we suggest the Maxwell construction revives the physical meaning effectively.Comment: 4 pages, 4figures, proceeding of Phase Transitions in Strongly Interacting Matter 18th International Nuclear Physics Divisional Conference of the EPS (NPDC18)Europhysics Conferenc

The appearance of quark matter in the core of hybrid stars is a fundamental issue in such compact stars. The central density of these stars is sufficiently high such that nuclear matter undergoes a further change into other exotic phases that consist of hyperons and quarks. However, the equation of state (EOS) for the high-density matter is still not clear and several recent observations have indicated the limitations of the EOSs; theoretical studies should try to elucidate the EOSs. It is believed that the inner regions of the stars should consist of a mixed hadron-quark phase. We study the mixed hadron-quark phase, taking into account finite-size effects, and find that that the mixed phase should be restricted to a narrower region. Therefore, a quark matter phase should appear in the central region.