Magnetic translation groups in an n-dimensional torus

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG on an n-dimensional torus is isomorphic to a central extension of a cyclic group Z_{nu_1} x ... x Z_{nu_{2l}} x T^m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG on a three-torus and apply the representation theory to three examples. We shortly describe a representation theory for a general n-torus. The MTG on an n-torus can be regarded as a generalization of the so-called noncommutative torus.Comment: 29 pages, LaTeX2e, title changed, re-organized, to be published in Journal of Mathematical Physic

Magnetized Accretion-Ejection Structures: 2.5D MHD simulations of continuous Ideal Jet launching from resistive accretion disks

We present numerical magnetohydrodynamic (MHD) simulations of a magnetized accretion disk launching trans-Alfvenic jets. These simulations, performed in a 2.5 dimensional time-dependent polytropic resistive MHD framework, model a resistive accretion disk threaded by an initial vertical magnetic field. The resistivity is only important inside the disk, and is prescribed as eta = alpha_m V_AH exp(-2Z^2/H^2), where V_A stands for Alfven speed, H is the disk scale height and the coefficient alpha_m is smaller than unity. By performing the simulations over several tens of dynamical disk timescales, we show that the launching of a collimated outflow occurs self-consistently and the ejection of matter is continuous and quasi-stationary. These are the first ever simulations of resistive accretion disks launching non-transient ideal MHD jets. Roughly 15% of accreted mass is persistently ejected. This outflow is safely characterized as a jet since the flow becomes super-fastmagnetosonic, well-collimated and reaches a quasi-stationary state. We present a complete illustration and explanation of the `accretion-ejection' mechanism that leads to jet formation from a magnetized accretion disk. In particular, the magnetic torque inside the disk brakes the matter azimuthally and allows for accretion, while it is responsible for an effective magneto-centrifugal acceleration in the jet. As such, the magnetic field channels the disk angular momentum and powers the jet acceleration and collimation. The jet originates from the inner disk region where equipartition between thermal and magnetic forces is achieved. A hollow, super-fastmagnetosonic shell of dense material is the natural outcome of the inwards advection of a primordial field.Comment: ApJ (in press), 32 pages, Higher quality version available at http://www-laog.obs.ujf-grenoble.fr/~fcass

Effect of Band Structure on the Symmetry of Superconducting States

Effects of the band structure on the symmetry of superconducting (SC) states are studied. For a square lattice system with a nearest-neighbor attractive interaction, SC states with various symmetries are found by changing the band structure, or, the shape of the Fermi surface. The spin-triplet ($(p_x + ip_y)$-wave) and spin-singlet ($d$- or s-wave) SC states, and states with their coexistence ($d + ip_y$, $s + ip_y$) can be stabilized within the same type of interaction. The stability of interlayer-pairing states with line nodes is also examined, and its relation to the SC state of Sr$_2$RuO$_4$ is discussed.Comment: 4 pages, 4 figure

Spin-triplet superconductivity due to antiferromagnetic spin-fluctuation in Sr_2RuO_4

A mechanism leading to the spin-triplet superconductivity is proposed based on the antiferromagnetic spin fluctuation. The effects of anisotropy in spin fluctuation on the Cooper pairing and on the direction of d vector are examined in the one-band Hubbard model with RPA approximation. The gap equations for the anisotropic case are derived and applied to Sr_2RuO_4. It is found that a nesting property of the Fermi surface together with the anisotropy leads to the triplet superconductivity with the d=z(sin{k_x}\pm isin{k_y}), which is consistent with experiments.Comment: 4 pages, 3 eps figures, revte

Cosmic ray short burst observed with the Global Muon Detector Network (GMDN) on June 22, 2015

We analyze the short cosmic ray intensity increase ("cosmic ray burst": CRB) on June 22, 2015 utilizing a global network of muon detectors and derive the global anisotropy of cosmic ray intensity and the density (i.e. the omnidirectional intensity) with 10-minute time resolution. We find that the CRB was caused by a local density maximum and an enhanced anisotropy of cosmic rays both of which appeared in association with Earth's crossing of the heliospheric current sheet (HCS). This enhanced anisotropy was normal to the HCS and consistent with a diamagnetic drift arising from the spatial gradient of cosmic ray density, which indicates that cosmic rays were drifting along the HCS from the north of Earth. We also find a significant anisotropy along the HCS, lasting a few hours after the HCS crossing, indicating that cosmic rays penetrated into the inner heliosphere along the HCS. Based on the latest geomagnetic field model, we quantitatively evaluate the reduction of the geomagnetic cut-off rigidity and the variation of the asymptotic viewing direction of cosmic rays due to a major geomagnetic storm which occurred during the CRB and conclude that the CRB is not caused by the geomagnetic storm, but by a rapid change in the cosmic ray anisotropy and density outside the magnetosphere.Comment: accepted for the publication in the Astrophysical Journa

Teaching controversial issues in Japan: An exploration of contextual gatekeeping

This qualitative case study sought to understand the extent to which Japanese high school Social Studies teachers grapple with controversial issues in their classrooms. Situated within a curricular-instructional gatekeeping framework, we conducted semi-structured interviews with eight respondents of varying backgrounds and schools in Okayama, Japan. The findings indicated that although the respondents believe they can teach controversial issues in their classrooms they generally do not because of specific contextual forces. Although we found controversial issue instruction to be generally moribund one respondent provided a rationale that reconceptualized exam preparation curriculum and instructio

Electronic theory for the normal state spin dynamics in Sr2_2RuO4_4: anisotropy due to spin-orbit coupling

Using a three-band Hubbard Hamiltonian we calculate within the random-phase-approximation the spin susceptibility, $\chi({\bf q},\omega)$, and NMR spin-lattice relaxation rate, 1/T$_1$, in the normal state of the triplet superconductor Sr$_2$RuO$_4$ and obtain quantitative agreement with experimental data. Most importantly, we find that due to spin-orbit coupling the out-of-plane component of the spin susceptibility $\chi^{zz}$ becomes at low temperatures two times larger than the in-plane one. As a consequence strong incommensurate antiferromagnetic fluctuations of the quasi-one-dimensional $xz$- and $yz$-bands point into the $z$-direction. Our results provide further evidence for the importance of spin fluctuations for triplet superconductivity in Sr$_2$RuO$_4$.Comment: revised versio

Electron-Phonon Interaction and Ultrasonic Attenuation in the Ruthenate and Cuprate superconductors

This article derives an electron-phonon interaction suitable for interpreting ultrasonic attenuation measurements in the ruthenate and cuprate superconductors. The huge anisotropy found experimentally (Lupien et al., 2001) in Sr2RuO4 in the normal state is accounted for in terms of the layered square-lattice structure of Sr2RuO4, and the dominant contribution to the attenuation in Sr2RuO4 is found to be due to electrons in the gamma band. The experimental data in the superconducting state is found to be inconsistent with vertical lines nodes in the gap in either (100) or (110) planes. Also, a general method, based on the use of symmetry, is developed to allow for the analysis of ultrasonic attenuation experiments in superconductors in which the electronic band structure is complicated or not known. Our results, both for the normal-state anisotropy, and relating to the positions of the gap nodes in the superconducting state, are different from those obtained from analyses using a more traditional model for the electron-phonon interaction in terms of an isotropic electron stress tensor. Also, a brief discussion of the ultrasonic attenuation in UPt3 is given.Comment: 12 pages. Comments have been added to the original version of this article showing how, for the ultrasonic attenuation for a hexagonal crystal (which must be isotropic with respect to rotations about the c axis) our approach reproduces the results of the traditional isotropic electron stress tensor mode