Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.Comment: 17 pages, 12 figure

Heavy-to-light scalar form factors from Muskhelishvili-Omn\`es dispersion relations

By solving the Muskhelishvili-Omn\`es integral equations, the scalar form factors of the semileptonic heavy meson decays $D\to\pi \bar \ell \nu_\ell$, $D\to \bar{K} \bar \ell \nu_\ell$, $\bar{B}\to \pi \ell \bar\nu_\ell$ and $\bar{B}_s\to K \ell \bar\nu_\ell$ are simultaneously studied. As input, we employ unitarized heavy meson-Goldstone boson chiral coupled-channel amplitudes for the energy regions not far from thresholds, while, at high energies, adequate asymptotic conditions are imposed. The scalar form factors are expressed in terms of Omn\`es matrices multiplied by vector polynomials, which contain some undetermined dispersive subtraction constants. We make use of heavy quark and chiral symmetries to constrain these constants, which are fitted to lattice QCD results both in the charm and the bottom sectors, and in this latter sector to the light-cone sum rule predictions close to $q^2=0$ as well. We find a good simultaneous description of the scalar form factors for the four semileptonic decay reactions. From this combined fit, and taking advantage that scalar and vector form factors are equal at $q^2=0$, we obtain $|V_{cd}|=0.244\pm 0.022$, $|V_{cs}|=0.945\pm 0.041$ and $|V_{ub}|=(4.3\pm 0.7)\times10^{-3}$ for the involved Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. In addition, we predict the following vector form factors at $q^2=0$: $|f_+^{D\to\eta}(0)|=0.01\pm 0.05$, $|f_+^{D_s\to K}(0)|=0.50 \pm 0.08$, $|f_+^{D_s\to\eta}(0)|=0.73\pm 0.03$ and $|f_+^{\bar{B}\to\eta}(0)|=0.82 \pm 0.08$, which might serve as alternatives to determine the CKM elements when experimental measurements of the corresponding differential decay rates become available. Finally, we predict the different form factors above the $q^2-$regions accessible in the semileptonic decays, up to moderate energies amenable to be described using the unitarized coupled-channel chiral approach.Comment: includes further discussions and references; matches the accepted versio

Accuracy control in ultra-large-scale electronic structure calculation

Numerical aspects are investigated in ultra-large-scale electronic structure calculation. Accuracy control methods in process (molecular-dynamics) calculation are focused. Flexible control methods are proposed so as to control variational freedoms, automatically at each time step, within the framework of generalized Wannier state theory. The method is demonstrated in silicon cleavage simulation with 10^2-10^5 atoms. The idea is of general importance among process calculations and is also used in Krylov subspace theory, another large-scale-calculation theory.Comment: 8 pages, 3 figures. To appear in J.Phys. Condens. Matter. A preprint PDF file in better graphics is available at http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htm

Theoretical analysis of magnetic coupling in sandwich clusters V_n(C_6H_6)_{n+1}

The mechanism of ferromagnetism stability in sandwich clusters V$_n$(C$_6$H$_6$)$_{n+1}$ has been studied by first-principles calculation and model analysis. It is found that each of the three types of bonds between V and benzene (Bz) plays different roles. V 3d$_{z^2}$ orbital, extending along the molecular axis, is weakly hybridized with Bz's HOMO-1 orbital to form the $\sigma$-bond. It is quite localized and singly occupied, which contributes 1$\mu_B$ to the magnetic moment but little to the magnetic coupling of neighboring V magnetic moments. The in-plane d$_{x^2-y^2}$, d$_{xy}$ orbitals are hybridized with the LUMO of Bz and constitute the $\delta$-bond. This hybridization is medium and crucial to the magnetic coupling though the $\delta$ states have no net contribution to the total magnetic moment. d$_{xz}$, d$_{yz}$ and HOMO of Bz form a quite strong $\pi$-bond to hold the molecular structure but they are inactive in magnetism because their energy levels are far away from the Fermi level. Based on the results of first-principles calculation, we point out that the ferromagnetism stability is closely related with the mechanism proposed by Kanamori and Terakura [J. Kanamori and K. Terakura, J. Phys. Soc. Jpn. 70, 1433 (2001)]. However, the presence of edge Bz's in the cluster introduces an important modification. A simple model is constructed to explain the essence of the physical picture.Comment: 16 pages, 7 figure

The Golden Channel at a Neutrino Factory revisited: improved sensitivities from a Magnetised Iron Neutrino Detector

This paper describes the performance and sensitivity to neutrino mixing parameters of a Magnetised Iron Neutrino Detector (MIND) at a Neutrino Factory with a neutrino beam created from the decay of 10 GeV muons. Specifically, it is concerned with the ability of such a detector to detect muons of the opposite sign to those stored (wrong-sign muons) while suppressing contamination of the signal from the interactions of other neutrino species in the beam. A new more realistic simulation and analysis, which improves the efficiency of this detector at low energies, has been developed using the GENIE neutrino event generator and the GEANT4 simulation toolkit. Low energy neutrino events down to 1 GeV were selected, while reducing backgrounds to the $10^{-4}$ level. Signal efficiency plateaus of ~60% for $\nu_\mu$ and ~70% for $\bar{\nu}_\mu$ events were achieved starting at ~5 GeV. Contamination from the $\nu_\mu\rightarrow \nu_\tau$ oscillation channel was studied for the first time and was found to be at the level between 1% and 4%. Full response matrices are supplied for all the signal and background channels from 1 GeV to 10 GeV. The sensitivity of an experiment involving a MIND detector of 100 ktonnes at 2000 km from the Neutrino Factory is calculated for the case of $\sin^2 2\theta_{13}\sim 10^{-1}$. For this value of $\theta_{13}$, the accuracy in the measurement of the CP violating phase is estimated to be $\Delta \delta_{CP}\sim 3^\circ - 5^\circ$, depending on the value of $\delta_{CP}$, the CP coverage at $5\sigma$ is 85% and the mass hierarchy would be determined with better than $5\sigma$ level for all values of $\delta_{CP}$

Systematically improvable optimized atomic basis sets for {\it ab inito} calculations

We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic orbital calculations and the converged plane wave calculations for dimer systems. The quality of the bases can be systematically improved by increasing the size of the bases within the same framework. The scheme is easy to implement and very flexible. We have done extensive tests of this scheme for wide variety of systems. The results show that the obtained atomic basis sets are very satisfactory for both accuracy and transferability

Fast diffusion of a Lennard-Jones cluster on a crystalline surface

We present a Molecular Dynamics study of large Lennard-Jones clusters evolving on a crystalline surface. The static and the dynamic properties of the cluster are described. We find that large clusters can diffuse rapidly, as experimentally observed. The role of the mismatch between the lattice parameters of the cluster and the substrate is emphasized to explain the diffusion of the cluster. This diffusion can be described as a Brownian motion induced by the vibrationnal coupling to the substrate, a mechanism that has not been previously considered for cluster diffusion.Comment: latex, 5 pages with figure

Large-scale electronic structure theory for simulating nanostructure process

Fundamental theories and practical methods for large-scale electronic structure calculations are given, in which the computational cost is proportional to the system size. Accuracy controlling methods for microscopic freedoms are focused on two practical solver methods, Krylov-subspace method and generalized-Wannier-state method. A general theory called the 'multi-solver' scheme is also formulated, as a hybrid between different solver methods. Practical examples are carried out in several insulating and metallic systems with 10^3-10^5 atoms. All the theories provide general guiding principles of constructing an optimal calculation for simulating nanostructure processes, since a nanostructured system consists of several competitive regions, such as bulk and surface regions, and the simulation is designed to reproduce the competition with an optimal computational cost.Comment: 19 pages, 6 figures. To appear in J. Phys. Cond. Matt. A preprint PDF file in better graphics is available at http://fujimac.t.u-tokyo.ac.jp/lses/index_e.htm