Dynamics of localized spins coupled to the conduction electrons with charge/spin currents

The effects of the charge/spin currents of conduction electrons on the dynamics of the localized spins are studied in terms of the perturbation in the exchange coupling $J_{K}$ between them. The equations of motion for the localized spins are derived exactly up to $O(J_{K}^2)$, and the equations for the two-spin system is solved numerically. It is found that the dynamics depends sensitively upon the relative magnitude of the charge and spin currents, i.e., it shows steady state, periodic motion, and even chaotic behavior. Extension to the multi-spin system and its implications including possible ``spin current detector'' are also discussed.Comment: 5 pages, 4 figures, REVTe

Active Brownian Motion in Threshold Distribution of a Coulomb Blockade Model

Randomly-distributed offset charges affect the nonlinear current-voltage property via the fluctuation of the threshold voltage of Coulomb blockade arrays. We analytically derive the distribution of the threshold voltage for a model of one-dimensional locally-coupled Coulomb blockade arrays, and propose a general relationship between conductance and the distribution. In addition, we show the distribution for a long array is equivalent to the distribution of the number of upward steps for aligned objects of different height. The distribution satisfies a novel Fokker-Planck equation corresponding to active Brownian motion. The feature of the distribution is clarified by comparing it with the Wigner and Ornstein-Uhlenbeck processes. It is not restricted to the Coulomb blockade model, but instructive in statistical physics generally.Comment: 4pages, 3figure

Limit structure of Future Null Infinity tangent -topology of the event horizon and gravitational wave tail-

We investigated the relation between the behavior of gravitational wave at late time and the limit structure of future null infinity tangent which will determine the topology of the event horizon far in the future. In the present article, we mainly consider a spacetime with two black holes. Although in most of cases, the black holes coalesce and its event horizon is topologically a single sphere far in the future, there are several possibilities that the black holes never coalesce and such exact solutions as examples. In our formulation, the tangent vector of future null infinity is, under conformal embedding, related to the number of black holes far in the future through the Poincar\'e-Hopf's theorem. Under the conformal embedding, the topology of event horizon far in the future will be affected by the geometrical structure of the future null infinity. In this article, we related the behavior of Weyl curvature to this limit behavior of the generator vector of the future null infinity. We show if Weyl curvature decays sufficiently slowly at late time in the neighborhood of future null infinity, two black holes never coalesce.Comment: 20 pages, 3 figures, accepted for publication in Class. Quant. Gra

Topological classification of black Hole: Generic Maxwell set and crease set of horizon

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat's principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structure of the Maxwell sets and the generic topologies of the spatial section of the horizon.Comment: 22 pages, 6 figure

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

Fast and stable method for simulating quantum electron dynamics

A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several computational techniques such as Suzuki's exponential product, Cayley's form, the finite differential method and an operator named adhesive operator. This method conserves the norm of the wavefunction, manages periodic conditions and adaptive mesh refinement technique, and is suitable for vector- and parallel-type supercomputers. Applying this method to some simple electron dynamics, we confirmed the efficiency and accuracy of the method for simulating fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure

Binary neutron-star mergers with Whisky and SACRA: First quantitative comparison of results from independent general-relativistic hydrodynamics codes

We present the first quantitative comparison of two independent general-relativistic hydrodynamics codes, the Whisky code and the SACRA code. We compare the output of simulations starting from the same initial data and carried out with the configuration (numerical methods, grid setup, resolution, gauges) which for each code has been found to give consistent and sufficiently accurate results, in particular in terms of cleanness of gravitational waveforms. We focus on the quantities that should be conserved during the evolution (rest mass, total mass energy, and total angular momentum) and on the gravitational-wave amplitude and frequency. We find that the results produced by the two codes agree at a reasonable level, with variations in the different quantities but always at better than about 10%.Comment: Published on Phys. Rev.

Improving the Cycle-life of Naphthoquinone-based Active Materials by Their Polymerization for Rechargeable Organic Batteries

AbstractTo increase the cycle-stability of rechargeable batteries using an organic positive-electrode material, we synthesized a polymer from a 5,8-dihydroxy-1,4-naphthoquinone (DHNQ) skeleton, which potentially undergoes a four-electron transfer redox reaction. The polymeric material (PDHNQ) was synthesized by the condensation reaction between DHNQ and formaldehyde under acidic media conditions. The initial capacity of the electrode using the monomer (DHNQ), 193 mAh/g, quickly decayed to 56 mAh/g after 100 cycles. On the other hand, the electrode incorporating the prepared PDHNQ showed the higher initial discharge capacity of 256 mAh/g and a longer cycle-life, retaining about 133 mAh/g after 100 cycles

Magnetohydrodynamics in full general relativity: Formulation and tests

A new implementation for magnetohydrodynamics (MHD) simulations in full general relativity (involving dynamical spacetimes) is presented. In our implementation, Einstein's evolution equations are evolved by a BSSN formalism, MHD equations by a high-resolution central scheme, and induction equation by a constraint transport method. We perform numerical simulations for standard test problems in relativistic MHD, including special relativistic magnetized shocks, general relativistic magnetized Bondi flow in stationary spacetime, and a longterm evolution for self-gravitating system composed of a neutron star and a magnetized disk in full general relativity. In the final test, we illustrate that our implementation can follow winding-up of the magnetic field lines of magnetized and differentially rotating accretion disks around a compact object until saturation, after which magnetically driven wind and angular momentum transport inside the disk turn on.Comment: 28 pages, to be published in Phys. Rev.

Stable Topologies of Event Horizon

In our previous work, it was shown that the topology of an event horizon (EH) is determined by the past endpoints of the EH. A torus EH (the collision of two EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In the present article, we examine the stability of the topology of the EH. We see that a simple case of a single spherical EH is unstable. Furthermore, in general, an EH with handles (a torus, a double torus, ...) is structurally stable in the sense of catastrophe theory.Comment: 21 pages, revtex, five figures containe