1,073 research outputs found
An Ext-Tor duality theorem, cohomological dimension, and applications
We provide a duality theorem between Ext and Tor modules over a
Cohen-Macaulay local ring possessing a canonical module, and use it to prove
some freeness criteria for finite modules. The applications include a
characterization of codimension three complete intersection ideals and progress
on a long-held multi-conjecture of Vasconcelos. By a similar technique, we
furnish another theorem which in addition makes use of the notion of
cohomological dimension and is mainly of interest in dimension one; as an
application, we show that the celebrated Huneke-Wiegand conjecture in the case
of complete intersections holds true provided that a single additional
condition is satisfied.Comment: 14 page
Vanishing of (co)homology, freeness criteria, and the Auslander-Reiten conjecture for Cohen-Macaulay Burch rings
We establish new results on (co)homology vanishing and Ext-Tor dualities, and
derive a number of freeness criteria for finite modules over Cohen-Macaulay
local rings. In the main application, we settle the long-standing
Auslander-Reiten conjecture for the class of Cohen-Macaulay Burch rings, among
other results toward this and related problems, e.g., the Tachikawa and
Huneke-Wiegand conjectures. We also derive results on further topics of
interest such as Cohen-Macaulayness of tensor products and Tor-independence,
and inspired by a paper of Huneke and Leuschke we obtain characterizations of
when a local ring is regular, or a complete intersection, or Gorenstein; for
the regular case, we describe progress on some classical differential problems,
e.g., the strong version of the Zariski-Lipman conjecture. Along the way, we
generalize several results from the literature and propose various questions.Comment: 25 pages. Submitted for publicatio
Some remarks on the spectral functions of the Abelian Higgs Model
We consider the unitary Abelian Higgs model and investigate its spectral
functions at one-loop order. This analysis allows to disentangle what is
physical and what is not at the level of the elementary particle propagators,
in conjunction with the Nielsen identities. We highlight the role of the
tadpole graphs and the gauge choices to get sensible results. We also introduce
an Abelian Curci-Ferrari action coupled to a scalar field to model a massive
photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a
modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary
nature directly from the spectral function viewpoint. This provides a
functional analogue of the Ojima observation in the canonical formalism: there
are ghost states with nonzero norm in the BRST-invariant states of the
Curci-Ferrari model.Comment: 32 pages, 12 figure
Eu2+ spin dynamics in the filled skutterudites EuM4Sb12 (M = Fe, Ru, Os)
We report evidence for a close relation between the thermal activation of the
rattling motion of the filler guest atoms, and inhomogeneous spin dynamics of
the Eu2+ spins. The spin dynamics is probed directly by means of Eu2+ electron
spin resonance (ESR), performed in both X-band (9.4 GHz) and Q-band (34 GHz)
frequencies in the temperature interval 4.2 < T < 300 K. A comparative study
with ESR measurements on the Beta-Eu8Ga16Ge30 clathrate compound is presented.
Our results point to a correlation between the rattling motion and the spin
dynamics which may be relevant for the general understanding of the dynamics of
cage systems.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.
Dirac-Surface-State-Dominated Spin to Charge Current Conversion in the Topological Insulator Films at Room Temperature
We report the spin to charge current conversation in an intrinsic topological
insulator (TI) film at room temperature. The spin
currents are generated in a thin layer of permalloy (Py) by two different
processes, spin pumping (SPE) and spin Seebeck effects (SSE). In the first we
use microwave-driven ferromagnetic resonance of the Py film to generate a SPE
spin current that is injected into the TI layer in
direct contact with Py. In the second we use the SSE in the longitudinal
configuration in Py without contamination by the Nernst effect made possible
with a thin NiO layer between the Py and layers.
The spin-to-charge current conversion is attributed to the inverse Edelstein
effect (IEE) made possible by the spin-momentum locking in the electron Fermi
contours due to the Rashba field. The measurements by the two techniques yield
very similar values for the IEE parameter, which are larger than the reported
values in the previous studies on topological insulators.Comment: 18 pages and 7 figure
Probing the Cosmic Distance Duality Relation with the Sunyaev-Zeldovich Effect, X-rays Observations and Supernovae Ia
The angular diameter distances toward galaxy clusters can be determined with
measurements of the Sunyaev-Zel'dovich effect and X-ray surface brightness
combined with the validity of the distance-duality relation, , where and are, respectively, the
luminosity and angular diameter distances. This combination enables us to probe
galaxy cluster physics or even to test the validity of the distance-duality
relation itself. We explore these possibilities based on two different, but
complementary approaches. Firstly, in order to constrain the possible galaxy
cluster morphologies, the validity of the distance-duality relation (DD
relation) is assumed in the CDM framework (WMAP7). Secondly, by
adopting a cosmological-model-independent test, we directly confront the
angular diameters from galaxy clusters with two supernovae Ia (SNe Ia)
subsamples (carefully chosen to coincide with the cluster positions). The
influence of the different SNe Ia light-curve fitters in the previous analysis
are also discussed. We assumed that is a function of the redshift
parametrized by two different relations: , and
, where is a constant parameter
quantifying the possible departure from the strict validity of the DD relation.
The statistical analysis presented here provides new evidence that the true
geometry of clusters is elliptical. We find that the two-light curve fitters
(SALT2 and MLCS2K2) present a statistically significant conflict, and a joint
analysis involving the different approaches suggests that clusters are endowed
with an elliptical geometry as previously assumed.Comment: 33 pages, 15 figures, some typos corrected, accepted for publication
in the Astronomy \& Astrophysic
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