Dynamical Structure Factors of the S=1/2 Bond-Alternating Spin Chain with a Next-Nearest-Neighbor Interaction in Magnetic Fields

The dynamical structure factor of the S=1/2 bond-alternating spin chain with a next-nearest-neighbor interaction in magnetic field is investigated using the continued fraction method based on the Lanczos algorithm. When the plateau exists on the magnetization curve, the longitudinal dynamical structure factor shows a large intensity with a periodic dispersion relation, while the transverse one shows a large intensity with an almost dispersionless mode. The periodicity and the amplitude of the dispersion relation in the longitudinal dynamical structure factor are sensitive to the coupling constants. The dynamical structure factor of the S=1/2 two-leg ladder in magnetic field is also calculated in the strong interchain-coupling regime. The dynamical structure factor shows gapless or gapful behavior depending on the wave vector along the rung.Comment: 8 pages, 4 figures, to appear in Journal of the Physical Society of Japan, vol. 69, no. 10, (2000

Polarized Neutron Inelastic Scattering Study of the Anisotropic Magnetic Fluctuations in the Quasi-1D Ising-like Antiferromagnet TlCoCl3_3

Polarized neutron inelastic scattering experiments have been carried out in the quasi-1D Ising-like antiferromagnet TlCoCl$_3$. We observed the longitudinal magnetic fluctuation $S_{zz} (Q, \omega)$ for the spin-wave excitation continuum, which has not been observed in the unpolarized neutron inelastic scattering experiments of the quasi-1D Ising-like antiferromagnets CsCoCl$_3$ and TlCoCl$_3$ so far, together with the transverse magnetic fluctuation $S_{xx} (Q, \omega)$. We compared both obtained intensities of $S_{xx} (Q, \omega)$ and $S_{zz} (Q, \omega)$ with the perturbation theory from the pure Ising limit by Ishimura and Shiba, and a semi-quantitative agreement was found.Comment: 5 pages, 5 figures, jpsj2.cls, to be published in J. Phys. Soc. Jpn. Vol. 75 (2006) No.

The IntraCluster Medium: An Invariant Stellar IMF

Evidence supporting the hypothesis of an invariant stellar Initial Mass Function is strong and varied. The intra-cluster medium in rich clusters of galaxies is one of the few contrary locations where recent interpretations of the chemical abundances have favoured an IMF that is biased towards massive stars, compared to the `normal' IMF. This interpretation hinges upon the neglect of Type Ia supernovae to the ICM enrichment, and a particular choice of the nucleosynthesis yields of Type II supernovae. We demonstrate here that when one adopts yields determined empirically from observations of Galactic stars, rather than the uncertain model yields, a self-consistent picture may be obtained with an invariant stellar IMF, and about half of the iron in the ICM being produced by Type Ia supernovae.Comment: 9 pages, LateX (aaspp4 macro), including one postscript figure. Accepted, ApJ Letter

Guardians Ad Litem as Surrogate Parents: Implication for Role Definition and Confidentiality

SALMON (Scalable Ab-initio Light–Mattersimulator for Optics and Nanoscience, http://salmon-tddft.jp) is a software package for the simulation of electron dynamics and optical properties of molecules, nanostructures, and crystalline solids based on first-principles time-dependent density functional theory. The core part of the software is the real-time, real-space calculation of the electron dynamics induced in molecules and solids by an external electric field solving the time-dependent Kohn–Sham equation. Using a weak instantaneous perturbing field, linear response properties such as polarizabilities and photoabsorptions in isolated systems and dielectric functions in periodic systems are determined. Using an optical laser pulse, the ultrafast electronic response that may be highly nonlinear in the field strength is investigated in time domain. The propagation of the laser pulse in bulk solids and thin films can also be included in the simulation via coupling the electron dynamics in many microscopic unit cells using Maxwell’s equations describing the time evolution of the electromagnetic fields. The code is efficiently parallelized so that it may describe the electron dynamics in large systems including up to a few thousand atoms. The present paper provides an overview of the capabilities of the software package showing several sample calculations. Program summary Program Title: SALMON: Scalable Ab-initio Light–Matter simulator for Optics and Nanoscience Program Files doi:http://dx.doi.org/10.17632/8pm5znxtsb.1 Licensing provisions: Apache-2.0 Programming language: Fortran 2003 Nature of problem: Electron dynamics in molecules, nanostructures, and crystalline solids induced by an external electric field is calculated based on first-principles time-dependent density functional theory. Using a weak impulsive field, linear optical properties such as polarizabilities, photoabsorptions, and dielectric functions are extracted. Using an optical laser pulse, the ultrafast electronic response that may be highly nonlinear with respect to the exciting field strength is described as well. The propagation of the laser pulse in bulk solids and thin films is considered by coupling the electron dynamics in many microscopic unit cells using Maxwell’s equations describing the time evolution of the electromagnetic field. Solution method: Electron dynamics is calculated by solving the time-dependent Kohn–Sham equation in real time and real space. For this, the electronic orbitals are discretized on a uniform Cartesian grid in three dimensions. Norm-conserving pseudopotentials are used to account for the interactions between the valence electrons and the ionic cores. Grid spacings in real space and time, typically 0.02 nm and 1 as respectively, determine the spatial and temporal resolutions of the simulation results. In most calculations, the ground state is first calculated by solving the static Kohn–Sham equation, in order to prepare the initial conditions. The orbitals are evolved in time with an explicit integration algorithm such as a truncated Taylor expansion of the evolution operator, together with a predictor–corrector step when necessary. For the propagation of the laser pulse in a bulk solid, Maxwell’s equations are solved using a finite-difference scheme. By this, the electric field of the laser pulse and the electron dynamics in many microscopic unit cells of the crystalline solid are coupled in a multiscale framework

Spin Wave Response in the Dilute Quasi-one Dimensional Ising-like Antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3

Inelastic neutron scattering profiles of spin waves in the dilute quasi-one-dimensional Ising-like antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3 have been investigated. Calculations of S^{xx}(Q,omega), based on an effective spin Hamiltonian, accurately describe the experimental spin wave spectrum of the 2J mode. The Q dependence of the energy of this spin wave mode follows the analytical prediction omega_{xx}(Q)=(2J)(1-5epsilon^{2}cos^{2}Qa+2epsilon^{2})^{1/2}, calculated by Ishimura and Shiba using perturbation theory.Comment: 13 pages, 4 figure

Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

Thermodynamic Properties and Elementary Excitations in Quantum Sine-Gordon Spin System KCuGaF6

Thermodynamic properties and elementary excitations in $S=1/2$ one-dimensional Heisenberg antiferromagnet KCuGaF$_6$ were investigated by magnetic susceptibility, specific heat and ESR measurements. Due to the Dzyaloshinsky-Moriya interaction with alternating $D$-vectors and/or the staggered $g$-tensor, the staggered magnetic field is induced when subjected to external magnetic field. Specific heat in magnetic field clearly shows the formation of excitation gap, which is attributed to the staggered magnetic field. The specific heat data was analyzed on the basis of the quantum sine-Gordon (SG) model. We observed many ESR modes including one soliton and three breather excitations characteristic of the quantum SG model.Comment: 4 pages, 5 figures, to appear in J. Phys. Soc. Jpn., vol. 76, no.

Dynamical Structure Factors of the Spin-1/2 XXZ Chain with Inverse-Square Exchange and Ising Anisotropy

The dynamical properties of the S=1/2 antiferromagnetic XXZ chain are studied by the exact diagonalization and the recursion method of finite systems up to 24 sites. Two types of the exchange interaction are considered: one is the nearest-neighbor type, and the other is the inverse-square one. As the Ising anisotropy becomes larger, there appears a noticeable difference in the transverse component S^{xx}(q,\omega) between the two types of the exchange. For the nearest-neighbor type, the peak frequency of S^{xx}(q,\omega) for each q approaches the center of the continuum spectrum. On the contrary, the peak frequency for the inverse-square type moves to the upper edge of the continuum, and separates from the continuum for the anisotropy larger than the threshold value. Whether the interaction between domain walls (solitons) is absent or repulsive in the Ising limit leads to this difference in the behavior of S^{xx}(q,\omega). In the longitudinal component S^{zz}(q,\omega), on the other hand, the feature of the dynamics is scarcely different between the two types. The energy gap and the static properties are also discussed.Comment: 10 pages. A hard copy of 16 figures is available on request. Submitted to J. Phys. Soc. Jp

A neutron scattering study of two-magnon states in the quantum magnet copper nitrate

We report measurements of the two-magnon states in a dimerized antiferromagnetic chain material, copper nitrate (Cu(NO3)2*2.5D2O). Using inelastic neutron scattering we have measured the one and two magnon excitation spectra in a large single crystal. The data are in excellent agreement with a perturbative expansion of the alternating Heisenberg Hamiltonian from the strongly dimerized limit. The expansion predicts a two-magnon bound state for q ~ (2n+1)pi*d which is consistent with the neutron scattering data.Comment: 11 pages of revtex style with 6 figures include