Statistical properties of antisymmetrized molecular dynamics for non-nucleon-emission and nucleon-emission processes

Statistical properties of the antisymmetrized molecular dynamics (AMD) are classical in the case of nucleon emission processes, while they are quantum mechanical for the processes without nucleon emission. We first clarify that there coexist mutually opposite two statistics in the AMD framework: One is the classical statistics of the motion of wave packet centroids and the other is the quantum statistics of the motion of wave packets which is described by the AMD wave function. We prove the classical statistics of wave packet centroids by using the framework of the microcanonical ensemble of the nuclear system. We show that the quantum statistics of wave packets emerges from the classical statistics of wave packet centroids. It is emphasized that the temperature of the classical statistics of wave packet centroids is different from the temperature of the quantum statistics of wave packets. We then explain that the statistical properties of AMD for nucleon emission processes are classical because nucleon emission processes in AMD are described by the motion of wave packet centroids. When we improve the description of the nucleon emission process so as to take into account the momentum fluctuation due to the wave packet spread, the AMD statistical properties for nucleon emission processes change drastically into quantum statistics. Our study of nucleon emission processes can be conversely regarded as giving another kind of proof of the fact that the statistics of wave packets is quantum mechanical while that of wave packet centroids is classical.Comment: 20 pages, LaTeX with revtex and epsf, uuenocded postscript figures, postscript version available at http://pearl.scphys.kyoto-u.ac.jp/~ono

Special values of shifted convolution Dirichlet series

In a recent important paper, Hoffstein and Hulse generalized the notion of Rankin-Selberg convolution $L$-functions by defining shifted convolution $L$-functions. We investigate symmetrized versions of their functions. Under certain mild conditions, we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and "mixed mock modular" forms.Comment: 18 pages, corrected slight error in main theorem and made according minor edits in Sections 3.4 and 3.

Statistical Properties of Fermionic Molecular Dynamics

Statistical properties of Fermionic Molecular Dynamics are studied. It is shown that, although the centroids of the single--particle wave--packets follow classical trajectories in the case of a harmonic oscillator potential, the equilibrium properties of the system are the quantum mechanical ones. A system of weakly interacting fermions as well as of distinguishable particles is found to be ergodic and the time--averaged occupation probabilities approach the quantum canonical ones of Fermi--Dirac and Boltzmann statistics, respectively.Comment: 16 pages, several postscript figures, uses 'epsfig.sty'. More information is available at http://www.gsi.de/~schnack/fmd.htm

Functional organic materials for electronics industries

Topics closely related with organic, high molecular weight material synthesis are discussed. These are related to applications such as display, recording, sensors, semiconductors, and I.C. correlation. New materials are also discussed. General principles of individual application are not included. Materials discussed include color, electrochromic, thermal recording, organic photoconductors for electrophotography, and photochromic materials

Nucleon Flow and Fragment Flow in Heavy Ion Reactions

The collective flow of nucleons and that of fragments in the 12C + 12C reaction below 150 MeV/nucleon are calculated with the antisymmetrized version of molecular dynamics combined with the statistical decay calculation. Density dependent Gogny force is used as the effective interaction. The calculated balance energy is about 100 MeV/nucleon, which is close to the observed value. Below the balance energy, the absolute value of the fragment flow is larger than that of nucleon flow, which is also in accordance with data. The dependence of the flow on the stochastic collision cross section and its origin are discussed. All the results are naturally understood by introducing the concept of two components of flow: the flow of dynamically emitted nucleons and the flow of the nuclear matter which contributes to both the flow of fragments and the flow of nucleons due to the statistical decay.Comment: 20 pages, PostScript figures, LaTeX with REVTeX and EPSF, KUNS 121

Magnetic-Field Induced Gap in One-Dimensional Antiferromagnet KCuGaF6_6

Magnetic susceptibility and specific heat measurements in magnetic fields were performed on an $S=1/2$ one-dimensional antiferromagnet KCuGaF$_6$. Exchange interaction was evaluated as $J/k_{\rm B}\simeq 100$ K. However, no magnetic ordering was observed down to 0.46 K. It was found that an applied magnetic field induces a staggered magnetic susceptibility obeying the Curie law and an excitation gap, both of which should be attributed to the antisymmetric interaction of the Dzyaloshinsky-Moriya type and/or the staggered $g$-tensor. With increasing magnetic field $H$, the gap increases almost in proportion to $H^{2/3}$.Comment: Submitted to Proceedings of Research in High Magnetic Fiel