Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity

A truncated moment formalism for general relativistic radiation hydrodynamics, based on the Thorne's moment formalism, is derived. The fluid rest frame is chosen to be the fiducial frame for defining the radiation moments. Then, zeroth-, first-, and second-rank radiation moments are defined from the distribution function with a physically reasonable assumption for it in the optically thin and thick limits. The source terms are written, focusing specifically on the neutrino transfer and neglecting higher harmonic angular dependence of the reaction angle. Finally, basic equations for a truncated moment formalism for general relativistic radiation hydrodynamics in a closed covariant form are derived assuming a closure relation among the radiation stress tensor, energy density, and energy flux, and a variable Eddington factor, which works well.Comment: 33 pages, 2 figures, to be published in Prog. Theor. Phy

Thermodynamic properties of the one-dimensional Kondo insulators studied by the density matrix renormalization group method

Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and specific heat are calculated down to T=0.1t for various exchange constants. The obtained results clearly show crossover behavior from the high temperature regime of nearly independent localized spins and conduction electrons to the low temperature regime where the two degrees of freedom couple strongly. The low temperature energy scales of the charge and spin susceptibilities are determined and shown to be equal to the quasiparticle gap and the spin gap, respectively, for weak exchange couplings.Comment: 4 pages, 3 Postscript figures, REVTeX, submitted to J. Phys. Soc. Jp

Gravitational waves from axisymmetrically oscillating neutron stars in general relativistic simulations

Gravitational waves from oscillating neutron stars in axial symmetry are studied performing numerical simulations in full general relativity. Neutron stars are modeled by a polytropic equation of state for simplicity. A gauge-invariant wave extraction method as well as a quadrupole formula are adopted for computation of gravitational waves. It is found that the gauge-invariant variables systematically contain numerical errors generated near the outer boundaries in the present axisymmetric computation. We clarify their origin, and illustrate it possible to eliminate the dominant part of the systematic errors. The best corrected waveforms for oscillating and rotating stars currently contain errors of magnitude $\sim 10^{-3}$ in the local wave zone. Comparing the waveforms obtained by the gauge-invariant technique with those by the quadrupole formula, it is shown that the quadrupole formula yields approximate gravitational waveforms besides a systematic underestimation of the amplitude of $O(M/R)$ where $M$ and $R$ denote the mass and the radius of neutron stars. However, the wave phase and modulation of the amplitude can be computed accurately. This indicates that the quadrupole formula is a useful tool for studying gravitational waves from rotating stellar core collapse to a neutron star in fully general relativistic simulations. Properties of the gravitational waveforms from the oscillating and rigidly rotating neutron stars are also addressed paying attention to the oscillation associated with fundamental modes

The Kondo-Hubbard model at half-filling

We have analyzed the antiferromagnetic (J>0) Kondo-Hubbard lattice with the band at half-filling by means of a perturbative approach in the strong coupling limit, the small parameter is an arbitrary tight-binding band. The results are valid for any band shape and any dimension. We have obtained the energies of elementary charge and spin excitations as well as the magnetic correlations in order to elucidate the magnetic and charge behavior of the Kondo lattice at half-filling. Finally, we have briefly analyzed the ferromagnetic case (J<0), which is shown to be equivalent to an effective antiferromagnetic Heisenberg model.Comment: 4 pages, Proceedings of SCES98/Pari

Thermodynamics of doped Kondo insulator in one dimension: Finite Temperature DMRG Study

The finite-temperature density-matrix renormalization-group method is applied to the one-dimensional Kondo lattice model near half filling to study its thermodynamics. The spin and charge susceptibilities and entropy are calculated down to T=0.03t. We find two crossover temperatures near half filling. The higher crossover temperature continuously connects to the spin gap at half filling, and the susceptibilities are suppressed around this temperature. At low temperatures, the susceptibilities increase again with decreasing temperature when doping is finite. We confirm that they finally approach to the values obtained in the Tomonaga-Luttinger (TL) liquid ground state for several parameters. The crossover temperature to the TL liquid is a new energy scale determined by gapless excitations of the TL liquid. The transition from the metallic phase to the insulating phase is accompanied by the vanishing of the lower crossover temperature.Comment: 4 pages, 7 Postscript figures, REVTe