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

Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation

On the basis of the antisymmetrized molecular dynamics (AMD) of wave packets for the quantum system, a novel model (called AMD-V) is constructed by the stochastic incorporation of the diffusion and the deformation of wave packets which is calculated by Vlasov equation without any restriction on the one-body distribution. In other words, the stochastic branching process in molecular dynamics is formulated so that the instantaneous time evolution of the averaged one-body distribution is essentially equivalent to the solution of Vlasov equation. Furthermore, as usual molecular dynamics, AMD-V keeps the many-body correlation and can naturally describe the fluctuation among many channels of the reaction. It is demonstrated that the newly introduced process of AMD-V has drastic effects in heavy ion collisions of 40Ca + 40Ca at 35 MeV/nucleon, especially on the fragmentation mechanism, and AMD-V reproduces the fragmentation data very well. Discussions are given on the interrelation among the frameworks of AMD, AMD-V and other microscopic models developed for the nuclear dynamics.Comment: 26 pages, LaTeX with revtex and epsf, embedded postscript figure

Antisymmetrized molecular dynamics with quantum branching processes for collisions of heavy nuclei

Antisymmetrized molecular dynamics (AMD) with quantum branching processes is reformulated so that it can be applicable to the collisions of heavy nuclei such as Au + Au multifragmentation reactions. The quantum branching process due to the wave packet diffusion effect is treated as a random term in a Langevin-type equation of motion, whose numerical treatment is much easier than the method of the previous papers. Furthermore a new approximation formula, called the triple-loop approximation, is introduced in order to evaluate the Hamiltonian in the equation of motion with much less computation time than the exact calculation. A calculation is performed for the Au + Au central collisions at 150 MeV/nucleon. The result shows that AMD almost reproduces the copious fragment formation in this reaction.Comment: 24 pages, 5 figures embedde

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

Fragmentation paths in dynamical models

We undertake a quantitative comparison of multi-fragmentation reactions, as modeled by two different approaches: the Antisymmetrized Molecular Dynamics (AMD) and the momentum-dependent stochastic mean-field (SMF) model. Fragment observables and pre-equilibrium (nucleon and light cluster) emission are analyzed, in connection to the underlying compression-expansion dynamics in each model. Considering reactions between neutron-rich systems, observables related to the isotopic properties of emitted particles and fragments are also discussed, as a function of the parametrization employed for the isovector part of the nuclear interaction. We find that the reaction path, particularly the mechanism of fragmentation, is different in the two models and reflects on some properties of the reaction products, including their isospin content. This should be taken into account in the study of the density dependence of the symmetry energy from such collisions.Comment: 11 pages, 13 figures, submitted to Phys. Rev.

Where do manufacturing firms locate their headquarters?

Firms’ headquarters [HQ] support their production activity, by gathering information and outsourcing business services, as well as, managing, evaluating, and coordinating internal firm activities. In search of a better location for these functions, firms often separate the HQ function physically from their production facilities and construct stand-alone HQs. By locating its HQ in a large, service oriented metro area away from its production facilities, a firm may be better able to out-source service functions in that local metro market and also to gather information about market conditions for their products. However if the firm locates the HQ away from its production activity, that increases the coordination costs in managing plant activities. In this paper we empirically analyze the trade-off of these two considerations.Corporations - Headquarters ; Industrial location ; Manufactures

Flexible control of the Peierls transition in metallic C60_{60} polymers

The metal-semiconductor transition of peanut-shaped fullerene (C$_{60}$) polymers is clarified by considering the electron-phonon coupling in the uneven structure of the polymers. We established a theory that accounts for the transition temperature $T_c$ reported in a recent experiment and also suggests that $T_c$ is considerably lowered by electron doping or prolonged irradiation during synthesis. The decrease in $T_c$ is an appealing phenomenon with regard to realizing high-conductivity C$_{60}$-based nanowires even at low temperatures.Comment: 3 pages, 3 figure

Nonlinear Doping of Cuprate Superconductors -- The case of Bi_2Sr_{2-x}La_xCuO_{6+\delta}

We analyze the hole doping mechanism in Bi_2Sr_{2-x}La_xCuO_{6+\delta} (BSLCO). The singular optimum around x=0.35 is found to be connected with a feedback between the doped CuO_2 layers and its dopant reactant [La^{3+}/Bi^{3+}-O_\delta] locking the number of doped holes preferentially on to the universal optimum n_opt=0.16.Comment: Typos correcte

On Shimura's decomposition

Let $k$ be an odd integer $\ge 3$ and $N$ a positive integer such that $4 \mid N$. Let $\chi$ be an even Dirichlet character modulo $N$. Shimura decomposes the space of half-integral weight cusp forms $S_{k/2}(N,\chi)$ as a direct sum of $S_0(N,\chi)$ (the subspace spanned by 1-variable theta- series) and $S_{k/2}(N,\chi,\phi)$ where $\phi$ runs through a certain family of integral weight newforms. The explicit computation of this decomposition is important for practical applications of a theorem of Waldspurger relating critical values of $L$-functions of quadratic twists of newforms of even weight to coefficients of modular forms of half-integral weight.Comment: 12 pages, to appear in the International Journal of Number Theor