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The effects of the $\Lambda$(1405) ($\Lambda^\ast$) on the structure of the multi-antikaonic nucleus (MKN), in which several $K^-$ mesons are embedded to form deeply bound states, are considered based on chiral symmetry combined with a relativistic mean-field theory. It is shown that additional attraction resulting from the $\Lambda^\ast$ pole has a sizable contribution to not only the density profiles for the nucleons and $K^-$ mesons but also the ground state energy of the $K^-$ mesons and binding energy of the MKN as the number of the embedded $K^-$ mesons increases., Comment: 4 pages, 3 figures, Talk presented at the 10th International Conference on Hypernuclear and Strange Particle Physics (Hyp-X), Tokai, Japan, Sept. 14-18, 2009. To be published in Nucl. Phys. A

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

Quantum molecular dynamics is applied to study the ground state properties of nuclear matter at subsaturation densities. Clustering effects are observed as to soften the equation of state at these densities. The structure of nuclear matter at subsaturation density shows some exotic shapes with variation of the density.

Liquid-gas phase transition is discussed in warm asymmetric nuclear matter. Some peculiar features are figured out from the viewpoint of the basic thermodynamics about the phase equilibrium. We treat the mixed phase of the binary system based on the Gibbs conditions. When the Coulomb interaction is included, the mixed phase is no more uniform and the sequence of the pasta structures appears. Comparing the results with those given by the simple bulk calculation without the Coulomb interaction, we extract specific features of the pasta structures at finite temperature.