Partially Solvable Anisotropic t-J Model with Long-Range Interactions

A new anisotropic t-J model in one dimension is proposed which has long-range hopping and exchange. This t-J model is only partially solvable in contrast to known integrable models with long-range interaction. In the high-density limit the model reduces to the XXZ chain with the long-range exchange. Some exact eigenfunctions are shown to be of Jastrow-type if certain conditions for an anisotropy parameter are satisfied. The ground state as well as the excitation spectrum for various cases of the anisotropy parameter and filling are derived numerically. It is found that the Jastrow-type wave function is an excellent trial function for any value of the anisotropy parameter.Comment: 10 pages, 3 Postscript figure

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.

Magnetic Excitations in the Quasi-1D Ising-like Antiferromagnet TlCoCl3_3

Neutron inelastic scattering measurements have been performed in order to investigate the magnetic excitations in the quasi-1D Ising-like antiferromagnet TlCoCl$_3$. We observed the magnetic excitation, which corresponds to the spin-wave excitation continuum corresponding to the domain-wall pair excitation in the 1D Ising-like antiferromagnet. According to the Ishimura-Shiba theory, we analyzed the observed spin-wave excitation, and the exchange constant $2J$ and the anistropy $\epsilon$ were estimated as 14.7 meV and 0.14 in TlCoCl$_3$, respectively.Comment: 2 pages, 3 figures, jpsj2.cls, to be published in J. Phys. Soc. Jpn. Vol.75 (2006) No.

Spiral solutions for a weakly anisotropic curvature flow equation

The presence of steps associated with screw dislocations plays a key role for the growth of crystal surfaces. In geometric model the motion of curves describing location of steps is governed by curvature flow equations with a driving force term. We show the existence of spiral-shaped solutions for such an equation when anisotropic effect is small. Such a spiral-shaped solution is ahown to be stable and unique up to translation of the time

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