4,718 research outputs found
About multiplicities and applications to Bezout numbers
Let denote a local Noetherian ring and
an ideal such that for a
finitely generated -module . Let \au = a_1,\ldots,a_d denote a system
of parameters of such that for . It follows that \chi := e_0(\au;M)
- c \cdot e_0(\mathfrak{q};M) \geq 0, where .
The main results of the report are a discussion when resp. to
describe the value of in some particular cases. Applications concern
results on the multiplicity e_0(\au;M) and applications to Bezout numbers.Comment: 11 pages, to appear Springer INdAM-Series, Vol. 20 (2017
A Millimeter-wave Galactic Plane Survey with the BICEP Polarimeter
In order to study inflationary cosmology and the Milky Way Galaxy's composition and magnetic field structure, Stokes I, Q, and U maps of the Galactic plane covering the Galactic longitude range 260° < ℓ < 340° in three atmospheric transmission windows centered on 100, 150, and 220 GHz are presented. The maps sample an optical depth 1 ≾ AV ≾ 30, and are consistent with previous characterizations of the Galactic millimeter-wave frequency spectrum and the large-scale magnetic field structure permeating the interstellar medium. The polarization angles in all three bands are generally perpendicular to those measured by starlight polarimetry as expected and show changes in the structure of the Galactic magnetic field on the scale of 60°. The frequency spectrum of degree-scale Galactic emission is plotted between 23 and 220 GHz (including WMAP data) and is fit to a two-component (synchrotron and dust) model showing that the higher frequency BICEP data are necessary to tightly constrain the amplitude and spectral index of Galactic dust. Polarized emission is detected over the entire region within two degrees of the Galactic plane, indicating the large-scale magnetic field is oriented parallel to the plane of the Galaxy. A trend of decreasing polarization fraction with increasing total intensity is observed, ruling out the simplest model of a constant Galactic magnetic field orientation along the line of sight in the Galactic plane. A generally increasing trend of polarization fraction with electromagnetic frequency is found, varying from 0.5%-1.5% at frequencies below 50 GHz to 2.5%-3.5% above 90 GHz. The effort to extend the capabilities of BICEP by installing 220 GHz band hardware is described along with analysis of the new band
Antiferroquadrupolar Order in the Magnetic Semiconductor TmTe
The physical properties of the antiferroquadrupolar state occurring in TmTe
below TQ=1.8 K have been studied using neutron diffraction in applied magnetic
fields. A field-induced antiferromagnetic component k = (1/2,1/2,1/2) is
observed and, from its magnitude and direction for different orientations of H,
an O(2,2) quadrupole order parameter is inferred. Measurements below TN ~= 0.5
K reveal that the magnetic structure is canted, in agreement with theoretical
predictions for in-plane antiferromagnetism. Complex domain repopulation
effects occur when the field is increased in the ordered phases, with
discontinuities in the superstructure peak intensities above 4 T.Comment: 6 pages, 6 figures, Presented at the International Conference on
Strongly Correlated Electrons with Orbital Degrees of Freedom (ORBITAL 2001),
September 11-14, 2001 (Sendai, JAPAN). To appear in: Journal of the Physical
Society of Japan (2002
Microscopic theory of quadrupolar ordering in TmTe
We have calculated the crystal electric field of TmTe (T>T_Q) and have
obtained that the ground state of a Tm 4f hole is the doublet in
agreement with Mossbauer experiments. We study the quadrupole interactions
arising from quantum transitions of 4f holes of Tm. An effective attraction is
found at the L point of the Brillouin zone, . Assuming that the
quadrupolar condensation involves a single arm of we show that
there are two variants for quadrupole ordering which are described by the space
groups C2/c and C2/m. The Landau free energy is derived in mean-field theory.
The phase transition is of second order. The corresponding quadrupole order
parameters are combinations of and components. The obtained
domain structure is in agreement with observations from neutron diffraction
studies for TmTe. Calculated lattice distortions are found to be different for
the two variants of quadrupole ordering. We suggest to measure lattice
displacements in order to discriminate between those two structures.Comment: 10 pages, 2 figures, 5 tables; accepted by PR
Spin dynamics and antiferromagnetic order in PrBa2Cu4O8 studied by Cu nuclear respnance
Results of the nuclear resonance experiments for the planar Cu sites in
PrBa2Cu4O8 are presented. The NMR spectrum at 1.5 K in zero magnetic field
revealed an internal field of 6.1 T, providing evidence for an
antiferromagnetic order of the planar Cu spins. This confirms that the CuO2
planes are insulating, therefore, the metallic conduction in this material is
entirely due to the one-dimensional zigzag Cu2O2 chains. The results of the
spin-lattice relaxation rates measured by zero field NQR above 245 K in the
paramagnetic state are explained by the theory for a Heisenberg model on a
square lattice.Comment: 4 pages, 2 figure
Studies on X-ray Thomson Scattering from Antiferroquadrupolar Order in TmTe
We study Thomson scattering from the antiferroquadrupole ordering phase in
TmTe. On the basis of the group theoretical treatment, we classify the
selection rules of the scattering intensity governed by the orientation of the
scattering vector G. Then, numerical verification is performed by invoking the
ground states which are deduced from a J=7/2 multiplet model. The obtained
intensity varies drastically depending on the magnitude and direction of G. We
also calculate the scattering intensities under the applied field for H//(001)
and (110). Their results behave differently when the orientation of G is
changed, which is ascribed to the difference of their primary order parameters;
O_{2}^{0} and O_{2}^{2} for H // (001) and (110), respectively. We make
critical comparisons between our results for TmTe and the experimental ones for
CeB_6. First, we assert that the intensities expected from TmTe at several
forbidden Bragg spots are sufficient enough to be experimentally detected.
Second, their intensities at (7/2,1/2,1/2) differ significantly and may be
attributed to the difference of the order parametersbetween the \Gamma_3-type
(O_{2}^{2} and O_{2}^{0}) and \Gamma_5-type (O_{yz}, O_{zx}, and O_{xy})
components, respectively.Comment: 18 pages, 3 figures, to be published in J. Phys. Soc. Jp
Fluctuation Effects on the Quadrupolar Ordering in Magnetic Field
Effects of magnetic field on the quadrupolar ordering are investigated with
inclusion of fluctuation of order parameters. For the simplest model with the
nearest-neighbor quadrupolar interaction, the transition temperature and the
specific heat are derived by the use of the recently proposed effective medium
theory. It is shown that magnetic field H has two competing effects on the
quadrupolar ordering; one is to encourage the ordering by suppressing the
fluctuation among different components of order parameters, and the other is to
block the ordering as in antiferromagnets. The former is found to be of order
H^2 and the latter of order H^4. Hence the fluctuation is suppressed for weak
fields, and the transition temperature increases with magnetic field. The
fluctuation effect is so strong that the entropy released at the quadrupolar
ordering is only about half of the full value ln 4 even without the Kondo
effect.Comment: 10 pages including 3 Postscript figure
Thermodynamical Study on the Heavy-Fermion Superconductor PrOs4Sb12: Evidence for Field-Induced Phase Transition
We report measurements of low-temperature specific heat on the 4f^2-based
heavy-fermion superconductor PrOs4Sb12. In magnetic fields above 4.5 T in the
normal state, distinct anomalies are found which demonstrate the existence of a
field-induced ordered phase (FIOP). The Pr nuclear specific heat indicates an
enhancement of the 4f magnetic moment in the FIOP. Utilizing a Maxwell
relation, we conclude that anomalous entropy, which is expected for a
single-site quadrupole Kondo model, is not concealed below 0.16 K in zero
field. We also discuss two possible interpretations of the Schottky-like
anomaly at ~3 K, i.e., a crystalline-field excitation or a hybridization gap
formation.Comment: 5 pages with 5 figures, a note with two references added in proo
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