The Lipkin Model in Many-Fermion System as an Example of the su(1,1) times su(1,1)-Algebraic Model

Following the idea, recently, proposed by the present authors for the two-level pairing model, the Lipkin model is reexamined. It is a natural generalization of the method already developed by the present authors with Kuriyama. This model is a schematic model for many-fermion system and obeys the su(2)-algebra. It is shown that the use of the Schwinger boson representation, the model is expressed in terms of the su(1,1) times su(1,1)-algebra and with the aid of the MYT mapping method, it is disguised from the orginal form in terms of the Holstein-Primakoff representation. Further, under various coherent states, the classical counterparts are derived. It is concluded that the Lipkin model can be treated in the common ring as that of the two-level pairing model.Comment: 22 pages, no figure, using PTPTeX.cl

A partial differential equation to express a business cycle :an implication for Japan's law interest policy

This study presents an equation of income derived from the Keynesian IS curve and the consumption Euler equation that explains the business cycle. Drawing on multi-period data from Japan, the model confirms the conventional wisdom that the appropriate policy response to an inflationary gap is to increase the interest rate when economic growth accelerates and decrease it when growth decelerates. However, the model indicates that to stabilize a deflationary gap, policymakers should decrease the interest rate when growth accelerates and increase it when growth decelerates. This prescription defies generations of conventional wisdom but fits the historical data remarkably well.BusinessCycle,Partial Differential Equation,Japan,Monetary Policy

Applications of synchrotron radiation to materials science: Diffraction imaging (topography) and microradiography

Synchrotron radiation sources are now available throughout the world. The use of hard X-ray radiation from these sources for materials science is described with emphasis on diffraction imaging for material characterization. With the availability of synchrotron radiation, real-time in situ measurements of dynamic microstructural phenomena have been started. This is a new area where traditional application of X-rays has been superseded. Examples are chosen from limited areas and are by no means exhaustive. The new emerging information will, no doubt, have great impact on materials science and engineering

Radiation hydrodynamical simulations of eruptive mass Loss from progenitors of Type Ibn/IIn supernovae

Observations suggest that some massive stars experience violent and eruptive mass loss associated with significant brightening that cannot be explained by hydrostatic stellar models. This event seemingly forms dense circumstellar matter (CSM). The mechanism of eruptive mass loss has not been fully explained. We focus on the fact that the timescale of nuclear burning gets shorter than the dynamical timescale of the envelope a few years before core collapse for some massive stars. To reveal the properties of the eruptive mass loss, we investigate its relation to the energy injection at the bottom of the envelope supplied by nuclear burning taking place inside the core. In this study, we do not specify the actual mechanism for transporting energy from the site of nuclear burning to the bottom of the envelope. Instead, we parameterize the amount of injected energy and the injection time and try to extract information on these parameters from comparisons with observations. We carried out 1-D radiation hydrodynamical simulations for progenitors of red, yellow, and blue supergiants, and Wolf-Rayet stars. We calculated the evolution of the progenitors with a public stellar evolution code. We obtain the light curve associated with the eruption, the amount of ejected mass, and the CSM distribution at the time of core-collapse. The energy injection at the bottom of the envelope of a massive star within a period shorter than the dynamical timescale of the envelope could reproduce some observed optical outbursts prior to the core-collapse and form the CSM, which can power an interaction supernova (SN) classified as type IIn.Comment: 10 pages, 16 figures, 2 tables, added references for section 1 and 4, added discussion in section 2 and 3, typos corrected, accepted for Astronomy and Astrophysic

On trace inequalities and their applications to noncommutative communication theory

Certain trace inequalities related to matrix logarithm are shown. These results enable us to give a partial answer of the open problem conjectured by A.S.Holevo. That is, concavity of the auxiliary function which appears in the random coding exponent as the lower bound of the quantum reliability function for general quantum states is proven in the case of $0\leq s\leq 1$.Comment: 8 page

A note on operator inequalities of Tsallis relative operator entropy

Tsallis relative operator entropy was defined as a parametric extension of relative operator entropy and the generalized Shannon inequalities were shown in the previous paper. After the review of some fundamental properties of Tsallis relative operator entropy, some operator inequalities related to Tsallis relative operator entropy are shown in the present paper. Our inequalities give the upper and lower bounds of Tsallis relative operator entropy. The operator equality on Tsallis relative operator entropy is also shown by considering the tensor product. This relation generalizes the pseudoadditivity for Tsallis entropy. As a corollary of our operator equality derived from the tensor product manipulation, we show several operator inequalities including the superadditivity and the subadditivity for Tsallis relative operator entropy. Our results are generalizations of the superadditivity and the subadditivity for Tsallis entropy.Comment: to appear in Linear Algebra App

Trace inequalities on a generalized Wigner-Yanase skew information

We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixure. In addition, several trace inequalities on our generalized Wigner-Yanase skew information are argued