Spin-1 effective Hamiltonian with three degenerate orbitals: An application to the case of V_2O_3

Motivated by recent neutron and x-ray observations in V_2O_3, we derive the effective Hamiltonian in the strong coupling limit of an Hubbard model with three degenerate t_{2g} states containing two electrons coupled to spin S = 1, and use it to re-examine the low-temperature ground-state properties of this compound. An axial trigonal distortion of the cubic states is also taken into account. Since there are no assumptions about the symmetry properties of the hopping integrals involved, the resulting spin-orbital Hamiltonian can be generally applied to any crystallographic configuration of the transition metal ion giving rise to degenerate t_{2g} orbitals. Specializing to the case of V_2O_3 we consider the antiferromagnetic insulating phase. We find two variational regimes, depending on the relative size of the correlation energy of the vertical pairs and the in-plane interaction energy. The former favors the formation of stable molecules throughout the crystal, while the latter tends to break this correlated state. We determine in both cases the minimizing orbital solutions for various spin configurations, and draw the corresponding phase diagrams. We find that none of the symmetry-breaking stable phases with the real spin structure presents an orbital ordering compatible with the magnetic space group indicated by very recent observations of non-reciprocal x-ray gyrotropy in V_2O_3. We do however find a compatible solution with very small excitation energy in two distinct regions of the phase space, which might turn into the true ground state of V_2O_3 due to the favorable coupling with the lattice. We illustrate merits and drawbacks of the various solutions and discuss them in relation to the present experimental evidence.Comment: 36 pages, 19 figure

Old stellar counter-rotating components in early-type galaxies from elliptical-spiral mergers

We investigate, by means of numerical simulations, the possibility of forming counter-rotating old stellar components by major mergers between an elliptical and a spiral galaxy. We show that counter-rotation can appear both in dissipative and dissipationless retrograde mergers, and it is mostly associated to the presence of a disk component, which preserves part of its initial spin. In turn, the external regions of the two interacting galaxies acquire part of the orbital angular momentum, due to the action of tidal forces exerted on each galaxy by the companion.Comment: 6 pages, 15 figures. Accepted on Astronomy & Astrophysic

X-ray Dichroism and the Pseudogap Phase of Cuprates

A recent polarized x-ray absorption experiment on the high temperature cuprate superconductor Bi2Sr2CaCu2O8 indicates the presence of broken parity symmetry below the temperature, T*, where a pseudogap appears in photoemission. We critically analyze the x-ray data, and conclude that a parity-breaking signal of the kind suggested is unlikely based on the crystal structures reported in the literature. Possible other origins of the observed dichroism signal are discussed. We propose x-ray scattering experiments that can be done in order to determine whether such alternative interpretations are valid or not.Comment: final version to be published in Phys Rev B: some calculational details added, clarification of XNLD contamination and biaxiality, more discussion on possible space groups and previous optics result

Star formation efficiency in galaxy interactions and mergers: a statistical study

We investigate the enhancement of star formation efficiency in galaxy interactions and mergers, by numerical simulations of several hundred galaxy collisions. All morphological types along the Hubble sequence are considered in the initial conditions of the two colliding galaxies, with varying bulge-to-disk ratios and gas mass fractions. Different types of orbits are simulated, direct and retrograde, according to the initial relative energy and impact parameter, and the resulting star formation history is compared to that occuring in the two galaxies when they are isolated. Our principal results are: (1) retrograde encounters have a larger star formation efficiency (SFE) than direct encounters; (2) the amount of gas available in the galaxy is not the main parameter governing the SFE in the burst phase; (3) there is an anticorrelation between the amplitude of the star forming burst and the tidal forces exerted per unit of time, which is due to the large amount of gas dragged outside the galaxy by tidal tails in strong interactions; (4) globally, the Kennicutt-Schmidt law is retrieved statistically for isolated galaxies, interacting pairs and mergers; (5) the enhanced star formation is essentially occurring in nuclear starbursts, triggered by inward gas flows driven by non-axisymmetries in the galaxy disks. Direct encounters develop more pronounced asymmetries than retrograde ones. Based on these statistical results, we derive general laws for the enhancement of star formation in galaxy interactions and mergers, as a function of the main parameters of the encounter.Comment: 22 pages, 37 figures, 4 tables. Accepted on Astronomy & Astrophysic

On the nature of the magnetic ground-state wave function of V_2O_3

After a brief historical introduction, we dwell on two recent experiments in the low-temperature, monoclinic phase of V_2O_3: K-edge resonant x-ray scattering and non-reciprocal linear dichroism, whose interpretations are in conflict, as they require incompatible magnetic space groups. Such a conflict is critically reviewed, in the light of the present literature, and new experimental tests are suggested, in order to determine unambiguously the magnetic group. We then focus on the correlated, non-local nature of the ground-state wave function, that is at the basis of some drawbacks of the LDA+U approach: we singled out the physical mechanism that makes LDA+U unreliable, and indicate the way out for a possible remedy. Finally we explain, by means of a symmetry argument related to the molecular wave function, why the magnetic moment lies in the glide plane, even in the absence of any local symmetry at vanadium sites.Comment: 7 pages, 1 figur

Discrete phase-space approach to mutually orthogonal Latin squares

We show there is a natural connection between Latin squares and commutative sets of monomials defining geometric structures in finite phase-space of prime power dimensions. A complete set of such monomials defines a mutually unbiased basis (MUB) and may be associated with a complete set of mutually orthogonal Latin squares (MOLS). We translate some possible operations on the monomial sets into isomorphisms of Latin squares, and find a general form of permutations that map between Latin squares corresponding to unitarily equivalent mutually unbiased sets. We extend this result to a conjecture: MOLS associated to unitarily equivalent MUBs will always be isomorphic, and MOLS associated to unitarily inequivalent MUBs will be non-isomorphic

Signatures of radial migration in barred galaxies: Azimuthal variations in the metallicity distribution of old stars

By means of N-body simulations, we show that radial migration in galaxy disks, induced by bar and spiral arms, leads to significant azimuthal variations in the metallicity distribution of old stars at a given distance from the galaxy center. Metals do not show an axisymmetric distribution during phases of strong migration. Azimuthal variations are visible during the whole phase of strong bar phase, and tend to disappear as the effect of radial migration diminishes, together with a reduction in the bar strength. These results suggest that the presence of inhomogeneities in the metallicity distribution of old stars in a galaxy disk can be a probe of ongoing strong migration. Such signatures may be detected in the Milky Way by Gaia (and complementary spectroscopic data), as well as in external galaxies, by IFU surveys like CALIFA and ATLAS3D. Mixing - defined as the tendency toward a homogeneous, azimuthally symmetric, stellar distribution in the disk - and migration turns out to be two distinct processes, the effects of mixing starting to be visible when strong migration is over.Comment: 8 pages, 10 figures, accepted for publication on Astronomy and Astrophysic

Low Luminosity States of the Black Hole Candidate GX 339-4. I. ASCA and Simultaneous Radio/RXTE Observations

We discuss a series of observations of the black hole candidate GX 339-4 in low luminosity, spectrally hard states. We present spectral analysis of three separate archival Advanced Satellite for Cosmology and Astrophysics (ASCA) data sets and eight separate Rossi X-ray Timing Explorer (RXTE) data sets. Three of the RXTE observations were strictly simultaneous with 843 MHz and 8.3-9.1 GHz radio observations. All of these observations have (3-9 keV) flux approximately < 10^{-9} ergs s^{-1} cm^{-2}. The ASCA data show evidence for an 6.4 keV Fe line with equivalent width 40 eV, as well as evidence for a soft excess that is well-modeled by a power law plus a multicolor blackbody spectrum with peak temperature 150-200 eV. The RXTE data sets also show evidence of an Fe line with equivalent widths 20-140 eV. Reflection models show a hardening of the RXTE spectra with decreasing X-ray flux; however, these models do not exhibit evidence of a correlation between the photon index of the incident power law flux and the solid angle subtended by the reflector. `Sphere+disk' Comptonization models and Advection Dominated Accretion Flow (ADAF) models also provide reasonable descriptions of the RXTE data. The former models yield coronal temperatures in the range 20-50 keV and optical depths of \tau ~ 3. The model fits to the X-ray data, however, do not simultaneously explain the observed radio properties. The most likely source of the radio flux is synchrotron emission from an extended outflow of size greater than O(10^7 GM/c^2).Comment: 18 pages in latex emulateapj.sty. Accepted for publication in the Astrophysical Journa