Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain

Recently a new integral equation describing the thermodynamics of the 1D Heisenberg model was discovered by Takahashi. Using the integral equation we have succeeded in obtaining the high temperature expansion of the specific heat and the magnetic susceptibility up to O((J/T)^{100}). This is much higher than those obtained so far by the standard methods such as the linked-cluster algorithm. Our results will be useful to examine various approximation methods to extrapolate the high temperature expansion to the low temperature region.Comment: 5 pages, 4 figures, 2 table

Magnetic Resonant X-Ray Scattering in KCuF3

We study the magnetic resonant x-ray scattering (RXS) spectra around the $K$ edge of Cu in KCuF$_3$ on the basis of an {\em ab initio} calculation. We use the full-potential linearlized augmented plane wave method in the LDA$+U$ scheme, and introduce the lattice distortion as inputs of the calculation. We obtain finite intensity on magnetic superlattice spots, about three orders of magnitude smaller than on orbital superlattice spots, by taking account of the spin-orbit interaction (SOI). No intensity appears without the SOI, indicating that the intensity arises not from the spin polarization but from the orbital polarization in $4p$ states. The present calculation reproduces well the experimental spectra as functions of photon energy and of azimuthal angle. We also calculate the RXS intensity on orbital superlattice spots. It is found that the intensity increases with increasing Jahn-Teller distortion. The spectra remain nearly the same in the nonmagnetic state given by the simple LDA, in which the orbital polarization in the 3d states is much smaller. This strongly suggests that the intensity on orbital spots is mainly controlled by the lattice distortion, not by the 3d orbital order itself.Comment: 7 pages, 8 figures, Submitted to PRB, RevTeX

Heavy Ion Collisions at the dawn of the LHC era

This is a proceeding of the CERN Latin American School of High-Energy physics that took place in the beautiful city of Natal, northern Brazil, in March 2011. In this paper I present a review of the main topics associated with the study of Heavy Ion Collisions, intended for students starting or interested in the field. It is impossible to summarize in a few pages the large amount of information that is available today, after a decade of operations of the RHIC accelerator and the beginning of the LHC operations. Thus, I had to choose some of the results and theories in order to present the main ideas and goals. All results presented here are from publicly available references, but some of the discussions and opinions are my personal view, where I have made that clear in the text.Comment: Proceeding of the CERN Latin American School of High-Energy physics, 201

Spectra, composition, and interactions of nuclei above 10 TeV using magnet-interferometric chambers

Although the SCIN-MAGIC experiment has, like all ASTROMAG and most other Attached Payload experiments, been 'deselected' from Space Station, it is expected that ultimately such emulsion chambers will be flown on the Station. Some brief studies are described which were made in support of the design efforts for such a program being conducted at NASA Marshall

Detection of extrasolar planets by the large deployable reflector

The best wavelength for observing Jupiter-size planetary companions to stars other than the Sun is one at which a planet's thermal emission is strongest; typically this would occur in the far-infrared region. It is assumed that the orbiting infrared telescope used is diffraction-limited so that the resolution of the planet from the central star is accomplished in the wings of the star's Airy pattern. Proxima Centauri, Barnard's Star, Wolf 359, and Epsilon Eridani are just a few of the many nearest main-sequence stars that could be studied with the large deployable relfector (LDR). The detectability of a planet improves for warmer planets and less luminous stars; therefore, planets around white dwarfs and those young planets which have sufficient internal gravitational energy release so as to cause a significant increase in their temperatures are considered. If white dwarfs are as old as they are usually assumed to be (5-10 billion yr), then only the nearest white dwarf (Sirius B) is within the range of LDR. The Ursa Major cluster and Perseu cluster are within LDR's detection range mainly because of their proximity and young age, respectively

Integrable Magnetic Model of Two Chains Coupled by Four-Body Interactions

An exact solution for an XXZ chain with four-body interactions is obtained and its phase diagram is determined. The model can be reduced to two chains coupled by four-body interactions, and it is shown that the ground state of the two-chain model is magnetized in part. Furthermore, a twisted four-body correlation function of the anti-ferromagnetic Heisenberg chain is obtained.Comment: 7 pages, LaTeX, to be published in J. Phys. Soc. Jpn., rederived the mode

The Free Energy and the Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

A nonlinear susceptibilities (the third derivative of a magnetization $m_S$ by a magnetic field $h$ ) of the $S$=1/2 ferromagnetic Heisenberg chain and the classical Heisenberg chain are calculated at low temperatures $T.$ In both chains the nonlinear susceptibilities diverge as $T^{-6}$ and a linear susceptibilities diverge as $T^{-2}.$ The arbitrary spin $S$ Heisenberg ferromagnet $[$ ${\cal H} = \sum_{i=1}^{N} \{ - J{\bf S}_{i} {\bf S}_{i+1} - (h/S) S_{i}^{z} \}$ $(J>0),$ $]$ has a scaling relation between $m_S,$ $h$ and $T:$ $m_S(T,h) = F( S^2 Jh/T^2).$ The scaling function $F(x)$=(2$x$/3)-(44$x^{3}$/135) + O($x^{5}$) is common to all values of spin $S.$Comment: 16 pages (revtex 2.0) + 6 PS figures upon reques

Transient Response Dynamic Module Modifications to Include Static and Kinetic Friction Effects

A methodology that supports forced transient response dynamic solutions when both static and kinetic friction effects are included in a structural system model is described. Modifications that support this type of nonlinear transient response solution are summarized for the transient response dynamics (TRD) NASTRAN module. An overview of specific modifications for the NASTRAN processing subroutines, INITL, TRD1C, and TRD1D, are described with further details regarding inspection of nonlinear input definitions to define the type of nonlinear solution required, along with additional initialization requirements and specific calculation subroutines to successfully solve the transient response problem. The extension of the basic NASTRAN nonlinear methodology is presented through several stages of development to the point where constraint equations and residual flexibility effects are introduced into the finite difference Newmark-Beta recurrsion formulas. Particular emphasis is placed on cost effective solutions for large finite element models such as the Space Shuttle with friction degrees of freedom between the orbiter and payloads mounted in the cargo bay. An alteration to the dynamic finite difference equations of motion is discussed, which allows one to include friction effects at reasonable cost for large structural systems such as the Space Shuttle. Data are presented to indicate the possible impact of transient friction loads to the payload designer for the Space Shuttle. Transient response solution data are also included, which compare solutions without friction forces and those with friction forces for payloads mounted in the Space Shuttle cargo bay. These data indicate that payload components can be sensitive to friction induced loads