Existence of covers with fixed ramification in positive characteristic

We discuss two elementary constructions for covers with fixed ramification in positive characteristic. As an application, we compute the number of certain classes of covers between projective lines branched at 4 points and obtain information on the structure of the Hurwitz curve parametrizing these covers

Roles of Bond Alternation in Magnetic Phase Diagram of RMnO3

In order to investigate nature of the antiferromagnetic structures in perovskite RMnO3, we study a Heisenberg J1-J2 model with bond alternation using analytical and numerical approaches. The magnetic phase diagram which includes incommensurate spiral states and commensurate collinear states is reproduced. We discuss that the magnetic structure with up-up-down-down spin configuration (E-type structure) and the ferroelectricity emerge cooperatively to stabilize this phase. Magnetoelastic couplings are crucial to understand the magnetic and electric phase diagram of RMnO3.Comment: 5 pages, 6 figure

Fulde-Ferrell-Larkin-Ovchinnikov State in the absence of a Magnetic Field

We propose that in a system with pocket Fermi surfaces, a pairing state with a finite total momentum q_tot like the Fulde-Ferrell-Larkin-Ovchinnikov state can be stabilized even without a magnetic field. When a pair is composed of electrons on a pocket Fermi surface whose center is not located at Gamma point, the pair inevitably has finite q_tot. To investigate this possibility, we consider a two-orbital model on a square lattice that can realize pocket Fermi surfaces and we apply fluctuation exchange approximation. Then, by changing the electron number n per site, we indeed find that such superconducting states with finite q_tot are stabilized when the system has pocket Fermi surfaces.Comment: 4 pages, 5 figure

Evidence for Jahn-Teller distortions at the antiferromagnetic transition in LaTiO3_3

LaTiO$_3$ is known as Mott-insulator which orders antiferromagnetically at $T_{\rm N}=146$ K. We report on results of thermal expansion and temperature dependent x-ray diffraction together with measurements of the heat capacity, electrical transport measurements, and optical spectroscopy in untwinned single crystals. At $T_{\rm N}$ significant structural changes appear, which are volume conserving. Concomitant anomalies are also observed in the dc-resistivity, in bulk modulus, and optical reflectivity spectra. We interpret these experimental observations as evidence of orbital order.Comment: 4 pages, 4 figures; published in Phys. Rev. Lett. 91, 066403 (2003

Origin of G-type Antiferromagnetism and Orbital-Spin Structures in LaTiO3{\rm LaTiO}_3

The possibility of the $D_{3d}$ distortion of ${\rm TiO}_6$ octahedra is examined theoretically in order to understand the origin of the G-type antiferromagnetism (AFM(G)) and experimentally observed puzzling properties of ${\rm LaTiO}_3$. By utilizing an effective spin and pseudospin Hamiltonian with the strong Coulomb repulsion, it is shown that AFM(G) state is stabilized through the lift of the $t_{2g}$-orbital degeneracy accompanied by a tiny $D_{3d}$-distortion . The estimated spin-exchange interaction is in agreement with that obtained by the neutron scattering. Moreover, the level-splitting energy due to the distortion can be considerably larger than the spin-orbit interaction even when the distortion becomes smaller than the detectable limit under the available experimental resolution. This suggests that the orbital momentum is fully quenched and the relativistic spin-orbit interaction is not effective in this system, in agreement with recent neutron-scattering experiment.Comment: 9 pages, 6 figure

Gamma-Ray Signatures of Supernovae and Hypernovae

We review the characteristics of nucleosynthesis and radioactivities in 'Hypernovae', i.e., supernovae with very large explosion energies ( \gsim 10^{52} ergs) and their $\gamma$-ray line signatures. We also discuss the $^{44}$Ti line $\gamma$-rays from SN1987A and the detectability with INTEGRAL. Signatures of hypernova nucleosynthesis are seen in the large [(Ti, Zn)/Fe] ratios in very metal poor stars. Radioactivities in hypernovae compared to those of ordinary core-collapse supernovae show the following characteristics: 1) The complete Si burning region is more extended, so that the ejected mass of $^{56}$Ni can be much larger. 2) Si-burning takes place in higher entropy and more $\alpha$-rich environment. Thus the $^{44}$Ti abundance relative to $^{56}$Ni is much larger. In aspherical explosions, $^{44}$Ti is even more abundant and ejected with velocities as high as $\sim$ 15,000 km s$^{-1}$, which could be observed in $\gamma$-ray line profiles. 3) The abundance of $^{26}$Al is not so sensitive to the explosion energy, while the $^{60}$Fe abundance is enhanced by a factor of $\sim$ 3.Comment: Invited talk at the ``GAMMA2001'' Symposium, April 4-6, 2001, Baltimore. To be published in ``Gamma-Ray Astronomy 2001'' (American Institute of Physics

G-type antiferromagnetism and orbital ordering due to the crystal field from the rare-earth ions induced by the GdFeO_3-type distortion in RTiO_3 with R=La, Pr, Nd and Sm

The origin of the antiferromagnetic order and puzzling properties of LaTiO_3 as well as the magnetic phase diagram of the perovskite titanates are studied theoretically. We show that in LaTiO_3, the t_{2g} degeneracy is eventually lifted by the La cations in the GdFeO_3-type structure, which generates a crystal field with nearly trigonal symmetry. This allows the description of the low-energy structure of LaTiO_3 by a single-band Hubbard model as a good starting point. The lowest-orbital occupation in this crystal field stabilizes the AFM(G) state, and well explains the spin-wave spectrum of LaTiO_3 obtained by the neutron scattering experiment. The orbital-spin structures for RTiO_3 with R=Pr, Nd and Sm are also accounted for by the same mechanism. We point out that through generating the R crystal field, the GdFeO_3-type distortion has a universal relevance in determining the orbital-spin structure of the perovskite compounds in competition with the Jahn-Teller mechanism, which has been overlooked in the literature. Since the GdFeO_3-type distortion is a universal phenomenon as is seen in a large number of perovskite compounds, this mechanism may also play important roles in other compounds of this type.Comment: 20 pages, 15 figure