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

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

Three-dimensional MHD Simulations of Jets from Accretion Disks

We report the results of 3-dimensional magnetohydrodynamic (MHD) simulations of a jet formation by the interaction between an accretion disk and a large scale magnetic field. The disk is not treated as a boundary condition but is solved self-consistently. To investigate the stability of MHD jet, the accretion disk is perturbed with a non-axisymmetric sinusoidal or random fluctuation of the rotational velocity. The dependences of the jet velocity $(v_z)$, mass outflow rate $(\dot{M}_w)$, and mass accretion rate $(\dot{M}_a)$ on the initial magnetic field strength in both non-axisymmetric cases are similar to those in the axisymmetric case. That is, $v_z \propto B_0^{1/3}$, $\dot{M}_w \propto B_0$ and $\dot{M}_a \propto B_0^{1.4}$ where $B_0$ is the initial magnetic field strength. The former two relations are consistent with the Michel's steady solution, $v_z \propto (B_0^2/\dot{M}_w)^{1/3}$, although the jet and accretion do not reach the steady state. In both perturbation cases, a non-axisymmetric structure with $m=2$ appears in the jet, where $m$ means the azimuthal wave number. This structure can not be explained by Kelvin-Helmholtz instability and seems to originate in the accretion disk. Non-axisymmetric modes in the jet reach almost constant levels after about 1.5 orbital periods of the accretion disk, while all modes in the accretion disk grow with oscillation. As for the angular momentum transport by Maxwell stress, the vertical component, $$, is comparable to the radial component,$$, in the wide range of initial magnetic field strength.Comment: Accepted for publication in ApJ. The pdf file with high resolution figures can be downloaded at http://www.kusastro.kyoto-u.ac.jp/~hiromitu/3j050806.pd

The Acceleration Mechanism of Resistive MHD Jets Launched from Accretion Disks

We analyzed the results of non-linear resistive magnetohydrodynamical (MHD) simulations of jet formation to study the acceleration mechanism of axisymmetric, resistive MHD jets. The initial state is a constant angular momentum, polytropic torus threaded by weak uniform vertical magnetic fields. The time evolution of the torus is simulated by applying the CIP-MOCCT scheme extended for resistive MHD equations. We carried out simulations up to 50 rotation period at the innermost radius of the disk created by accretion from the torus. The acceleration forces and the characteristics of resistive jets were studied by computing forces acting on Lagrangian test particles. Since the angle between the rotation axis of the disk and magnetic field lines is smaller in resistive models than in ideal MHD models, magnetocentrifugal acceleration is smaller. The effective potential along a magnetic field line has maximum around $z \sim 0.5r_0$ in resistive models, where $r_0$ is the radius where the density of the initial torus is maximum. Jets are launched after the disk material is lifted to this height by pressure gradient force. Even in this case, the main acceleration force around the slow magnetosonic point is the magnetocentrifugal force. The power of the resistive MHD jet is comparable to the mechanical energy liberated in the disk by mass accretion. Joule heating is not essential for the formation of jets.Comment: 15 pages, 15 figures, 1 table, accepted for publication in Ap

Temporal 1/f^\alpha Fluctuations from Fractal Magnetic Fields in Black Hole Accretion Flow

Rapid fluctuation with a frequency dependence of $1/f^{\alpha}$ (with $\alpha \simeq 1 - 2$) is characteristic of radiation from black-hole objects. Its origin remains poorly understood. We examine the three-dimensional magnetohydrodynamical (MHD) simulation data, finding that a magnetized accretion disk exhibits both $1/f^\alpha$ fluctuation (with $\alpha \simeq 2$) and a fractal magnetic structure (with the fractal dimension of $D \sim 1.9$). The fractal field configuration leads reconnection events with a variety of released energy and of duration, thereby producing $1/f^\alpha$ fluctuations.Comment: 5 pages, 4 figures. Accepted for publication in PASJ Letters, vol. 52 No.1 (Feb 2000

Possible explanation for star-crushing effect in binary neutron star simulations

A possible explanation is suggested for the controversial star-crushing effect seen in numerical simulations of inspiraling neutron star binaries by Wilson, Mathews and Marronetti (WMM). An apparently incorrect definition of momentum density in the momentum constraint equation used by WMM gives rise to a post-1-Newtonian error in the approximation scheme. We show by means of an analytic, post-1-Newtonian calculation that this error causes an increase of the stars' central densities which is of the order of several percent when the stars are separated by a few stellar radii, in agreement with what is seen in the simulations.Comment: 4 pages, 1 figure, uses revetx macros, minor revision

New criterion for direct black hole formation in rapidly rotating stellar collapse

We study gravitational collapse of rapidly rotating relativistic polytropes of the adiabatic index $\Gamma = 1.5$ and 2, in which the spin parameter $q \equiv J/M^{2} > 1$ where $J$ and $M$ are total angular momentum and gravitational mass, in full general relativity. First, analyzing initial distributions of the mass and the spin parameter inside stars, we predict the final outcome after the collapse. Then, we perform fully general relativistic simulations on assumption of axial and equatorial symmetries and confirm our predictions. As a result of simulations, we find that in contrast with the previous belief, even for stars with $q > 1$, the collapse proceeds to form a seed black hole at central region, and the seed black hole subsequently grows as the ambient fluids accrete onto it. We also find that growth of angular momentum and mass of the seed black hole can be approximately determined from the initial profiles of the density and the specific angular momentum. We define an effective spin parameter at the central region of the stars, $q_{c}$, and propose a new criterion for black hole formation as q_{c} \alt 1. Plausible reasons for the discrepancy between our and previous results are clarified.Comment: submitted to PR