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 (Bi0.22Sb0.78)2Te3(Bi_{0.22}Sb_{0.78})_2Te_3 Films at Room Temperature

We report the spin to charge current conversation in an intrinsic topological insulator (TI) $(Bi_{0.22}Sb_{0.78})_2Te_3$ 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 $(Bi_{0.22}Sb_{0.78})_2Te_3$ 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 $(Bi_{0.22}Sb_{0.78})_2Te_3$ 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, $D_L(z) (1 + z)^{2}/D_{A}(z) = 1$, where $D_L(z)$ and $D_A(z)$ 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 $\Lambda$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 $\eta$ is a function of the redshift parametrized by two different relations: $\eta(z) = 1 + \eta_{0}z$, and $\eta(z)=1 + \eta_{0}z/(1+z)$, where $\eta_0$ 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