Comparison of the relative entropy of entanglement and negativity

It is well known that for two qubits the upper bounds of the relative entropy of entanglement (REE) for a given concurrence as well as the negativity for a given concurrence are reached by pure states. We show that, by contrast, there are two-qubit mixed states for which the REE for some range of a fixed negativity is higher than that for pure states. Moreover, we demonstrate that a mixture of a pure entangled state and pure separable state orthogonal to it is likely to give the maximal REE. By noting that the negativity is a measure of entanglement cost under operations preserving positivity of partial transpose, our results provide an explicit example of operations such that, even though the entanglement cost for an exact preparation is the same, the entanglement of distillation of a mixed state can exceed that of pure states. This means that the entanglement manipulation via a pure state can result in a larger entanglement loss than that via a mixed state.Comment: 8 pages, 3 figure

Observation of Jonscher Law in AC Hopping Conduction of Electron-Doped Nanoporous Crystal 12CaO7Al2O3 in THz Frequency Range

We have performed terahertz time-domain spectroscopy of carrier-doped nanoporous crystal 12CaO7Al2O3 showing the Mott variable range hopping at room temperature. The real part of the dielectric constant clearly demonstrates the nature of localized carriers. The frequency dependence of both the real and imaginary parts of the dielectric constant can be simply explained by assuming two contributions: a dielectric response by the parent compound with no carriers and an AC hopping conduction with the Jonscher law generally reported up to GHz range. The possible obedience to the Jonscher law in the THz range suggests a relaxation time of the hopping carriers much faster than 1ps in the carrier-doped 12CaO7Al2O3.Comment: 4pages 3figures. to be published in Phys. Rev.

Non-Thermal Emission from Relativistic Electrons in Clusters of Galaxies: A Merger Shock Acceleration Model

We have investigated evolution of non-thermal emission from relativistic electrons accelerated at around the shock fronts during merger of clusters of galaxies. We estimate synchrotron radio emission and inverse Compton scattering of cosmic microwave background photons from extreme ultraviolet (EUV) to hard X-ray range. The hard X-ray emission is most luminous in the later stage of merger. Both hard X-ray and radio emissions are luminous only while signatures of merging events are clearly seen in thermal intracluster medium (ICM). On the other hand, EUV radiation is still luminous after the system has relaxed. Propagation of shock waves and bulk-flow motion of ICM play crucial roles to extend radio halos. In the contracting phase, radio halos are located at the hot region of ICM, or between two substructures. In the expanding phase, on the other hand, radio halos are located between two ICM hot regions and shows rather diffuse distribution.Comment: 19 pages, 5 figures, accepted for publication in Ap

An LP-based inconsistency monitoring of pairwise comparison matrices

A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied in the process of filling in the matrix as the decision maker gets automatic feedback. As soon as a serious error occurs among the matrix elements, even due to a misprint, a significant increase in the inconsistency index is reported. The high inconsistency may be alarmed not only at the end of the process of filling in the matrix but also during the completion process. Numerical examples are also provided

Multiparticle entanglement manipulation under positive partial transpose preserving operations

Published versio

Relative entropy of entanglement of a kind of two qubit entangled states

We in this paper strictly prove that some block diagonalizable two qubit entangled state with six none zero elements reaches its quantum relative entropy entanglement by the a separable state having the same matrix structure. The entangled state comprises local filtering result state as a special case.Comment: 5 page

Off-Center Mergers of Clusters of Galaxies and Nonequipartition of Electrons and Ions in Intracluster Medium

We investigate the dynamical evolution of clusters of galaxies and their observational consequences during off-center mergers, explicitly considering the relaxation process between ions and electrons in intracluster medium by N-body and hydrodynamical simulations. In the contracting phase a bow shock is formed between the two subclusters. The observed temperature between two peaks in this phase depends on the viewing angle even if the geometry of the system seems to be very simple like head-on collisions. Around the most contracting epoch, when we observe merging clusters nearly along the collision axis, they look like spherical relaxed clusters with large temperature gradients. In the expanding phase, spiral bow shocks occur. As in head-on mergers, the electron temperature is significantly lower than the plasma mean one especially in the post-shock regions in the expanding phase. When the systems have relatively large angular momentum, double-peak structures in the X-ray images can survive even after the most contracting epoch. Morphological features in both X-ray images and electron temperature distribution characteristic to off-center mergers are seriously affected by the viewing angle. When the clusters are observed nearly along the collision axis, the distribution of galaxies' line-of-sight (LOS) velocities is a good indicator of mergers. In the contracting phase, an negative kurtosis and a large skewness are expected for nearly equal mass collisions and rather different mass ones, respectively. To obtain statistically significant results, about 1000 galaxies' LOS velocities are required. For nearby clusters ($z<0.05$), large redshift surveys such as 2dF will enable us to study merger dynamics.Comment: 21 pages, 7 figures. Accepted for publication in Ap

Two-Temperature Intracluster Medium in Merging Clusters of Galaxies

We investigate the evolution of intracluster medium during a cluster merger, explicitly considering the relaxation process between the ions and electrons by N-body and hydrodynamical simulations. When two subclusters collide each other, a bow shock is formed between the centers of two substructures and propagate in both directions along the collision axis. The shock primarily heats the ions because the kinetic energy of an ion entering the shock is larger than that of an electron by the ratio of masses. In the post-shock region the energy is transported from the ions to electrons via Coulomb coupling. However, since the energy exchange timescale depends both on the gas density and temperature, distribution of electron temperature becomes more complex than that of the plasma mean temperature, especially in the expanding phase. After the collision of two subclusters, gas outflow occurs not only along the collision axis but also in its perpendicular direction. The gas which is originally located in the central part of the subclusters moves both in the parallel and perpendicular directions. Since the equilibrium timescale of the gas along these directions is relatively short, temperature difference between ions and electrons is larger in the directions tilted by the angles of $\pm 45^\circ$ with respect to the collision axis. The electron temperature could be significantly lower that the plasma mean temperature by $\sim 50$ at most. The significance of our results in the interpretation of X-ray observations is briefly discussed.Comment: 20 pages, 11 figures, Accepted for publication in Ap