We present the results of two-temperature magnetohydrodynamic simulations of the propagation of sub-relativistic jets of active galactic nuclei. The dependence of the electron and ion temperature distributions on the fraction of electron heating fe a
t the shock front is studied for fe=0, 0.05, and 0.2. Numerical results indicate that in sub-relativistic, rarefied jets, the jet plasma crossing the terminal shock forms a hot, two-temperature plasma in which the ion temperature is higher than the electron temperature. The two-temperature plasma expands and forms a backflow referred to as a cocoon, in which the ion temperature remains higher than the electron temperature for longer than 100 Myr. Electrons in the cocoon are continuously heated by ions through Coulomb collisions, and the electron temperature thus remains at Te > 10^9 K in the cocoon. X-ray emissions from the cocoon are weak because the electron number density is low. Meanwhile, soft X-rays are emitted from the shocked intracluster medium surrounding the cocoon. Mixing of the jet plasma and the shocked intracluster medium through the Kelvin--Helmholtz instability at the interface enhances X-ray emissions around the contact discontinuity between the cocoon and shocked intracluster medium.
We consider repulsively-interacting cold fermionic atoms loaded on an optical ladder lattice in a trapping potential. The density-matrix renormalization-group method is used to numerically calculate the ground state for systematically varied values o
f interaction U and spin imbalance p in the Hubbard model on the ladder. The system exhibits rich structures, where a fully spin polarized phase, spatially separated from other domains in the trapping potential, appears for large enough U and p. The phase-separated ferromagnetism can be captured as a real-space image of the energy gap between the ferromagnetic and other states arising from a combined effect of Nagaokas ferromagnetism extended to the ladder and the density dependence of the energy separation between competing states. We also predict how to maximize the ferromagnetic region.
We present new thermal equilibrium solutions for optically thin and thick disks incorporating magnetic fields. The purpose of this paper is to explain the bright hard state and the bright/slow transition observed in the rising phases of outbursts in
BHCs. On the basis of the results of 3D MHD simulations, we assume that magnetic fields inside the disk are turbulent and dominated by the azimuthal component and that the azimuthally averaged Maxwell stress is proportional to the total pressure. We prescribe the magnetic flux advection rate to determine the azimuthal magnetic flux at a given radius. We find magnetically supported, thermally stable solutions for both optically thin and thick disks, in which the heating enhanced by the strong magnetic field balances the radiative cooling. The temperature in a low-$beta$ disk is lower than that in an ADAF/RIAF but higher than that in a standard disk. We also study the radial dependence of the thermal equilibrium solutions. The optically thin, low-$beta$ branch extends to $ dot M gtrsim 0.1 {dot M}_{rm Edd}$, in which the temperature anti-correlates with the mass accretion rate. Thus optically thin low-$beta$ disks can explain the bright hard state. Optically thick, low-$beta$ disks have the radial dependence of the effective temperature $T_{rm eff} propto varpi^{-3/4}$. Such disks will be observed as staying in a high/soft state. Furthermore, limit cycle oscillations between an optically thick low-$beta$ disk and a slim disk will occur because the optically thick low-$beta$ branch intersects with the radiation pressure dominated standard disk branch. These limit cycle oscillations will show a smaller luminosity variation than that between a standard disk and a slim disk.
In order to demonstrate that atomic Fermi gas is a good experimental reality in studying unsolved problems in frustrated interacting-spin systems, we numerically examine the Mott core state emerged by loading two-component atomic Fermi gases on trian
gular optical lattices. Consequently, we find that plateau like structures are observable in the Mott core polarization as a function of the population imbalance. These plateau states are caused by a flexibility that the surrounding metallic region absorbs the excess imbalance to keep the plateau states inside the Mott core. We also find spin patterns peculiar to the plateau states inside the Mott core.
We investigate effects of pseudo-spin population imbalance on Mott phases in 1D trapped two-component atomic Fermi gases loaded on optical lattices based on the repulsive Hubbard model in harmonic traps. By using the density matrix renormalization gr
oup method, we numerically calculate density profiles of each component and clarify the pseudo-spin magnetism. Consequently, we find that all the features from weakly imbalance to fully polarized cases are well described by S=1/2 antiferromagnetic Heisenberg chain under magnetic field. These results indicate that the Mott phases offer experimental stages for studying various interacting spin systems.
We investigate effects of optical lattice potential in one- and two-dimensional two-component trapped Fermi gases with population imbalances. Using the exact diagonalization and the density matrix renormalization group methods complementarily, we cal
culate the atom density profile from the ground state many-body wavefunction as a function of attractive interaction strength for various population imbalances. The numerical results reveal that although a phase separation between the superfluid core and the shell cloud of excess atoms occurs as observed in experiments without the optical lattice, the population imbalance generally remains in the core region in contrast to the non-lattice cases. The essence of the numerical results in a strong attractive regime can be explained by an effective model composed of Cooper pairs and excess major fermions.
We suggest that box shape trap enables to observe intrinsic properties of the repulsive Hubbard model in a fixed doping in contrast to the harmonic trap bringing about spatial variations of atom density profiles. In order to predict atomic density pr
ofile under the box trap, we apply the directly-extended density-matrix renormalization group method to 4-leg repulsive Hubbard model with the open boundary condition. Consequently, we find that stripe formation is universal in a low hole doping range and the stripe sensitively changes its structure with variations of $U/t$ and the doping rate. A remarkable change is that a stripe formed by a hole pair turns to one by a bi-hole pair when entering a limited strong $U/t$ range. Furthermore, a systematic calculation reveals that the Hubbard model shows a change from the stripe to the Friedel like oscillation with increasing the doping rate.
We study the Josephson effect between a conventional s-wave superconductor and a non-centrosymmetric superconductor with Rashba spin-orbit coupling. Rashba spin-orbit coupling affects the Josephson pair tunneling in a characteristic way. The Josephso
n coupling can be decomposed into two parts, a `spin-singlet-like and a `spin-triplet-like component. The latter component can lead to shift of the Josephson phase by pi relative to the former coupling. This has important implications on interference effects and may explain some recent experimental results for the Al/CePt3Si junction.
We parallelize density-matrix renormalization group to directly extend it to 2-dimensional ($n$-leg) quantum lattice models. The parallelization is made mainly on the exact diagonalization for the superblock Hamiltonian since the part requires an eno
rmous memory space as the leg number $n$ increases. The superblock Hamiltonian is divided into three parts, and the correspondent superblock vector is transformed into a matrix, whose elements are uniformly distributed into processors. The parallel efficiency shows a high rate as the number of the states kept $m$ increases, and the eigenvalue converges within only a few sweeps in contrast to the multichain algorithm.
We present the results of three-dimensional global magnetohydrodynamic (MHD) simulations of the Parker-shearing instability in a differentially rotating torus initially threaded by toroidal magnetic fields. An equilibrium model of magnetized torus is
adopted as an initial condition. When $beta_0 = P_{rm gas}/P_{rm mag} sim 1$ at the initial state, magnetic flux buoyantly escapes from the disk and creates loop-like structures similar to those in the solar corona. Inside the torus, growth of non-axisymmetric magneto-rotational (or Balbus & Hawley) instability generates magnetic turbulence. Magnetic field lines are tangled in small scale but in large scale they show low azimuthal wave number spiral structure. After several rotation period, the system oscillates around a state with $beta sim 5$. We found that magnetic pressure dominated ($beta < 1$) filaments are created in the torus. The volume filling factor of the region where $beta leq 0.3$ is 2-10%. Magnetic energy release in such low-$beta$ regions may lead to violent flaring activities in accretion disks and in galactic gas disks.
