Dark energy, non-minimal couplings and the origin of cosmic magnetic fields

In this work we consider the most general electromagnetic theory in curved space-time leading to linear second order differential equations, including non-minimal couplings to the space-time curvature. We assume the presence of a temporal electromagnetic background whose energy density plays the role of dark energy, as has been recently suggested. Imposing the consistency of the theory in the weak-field limit, we show that it reduces to standard electromagnetism in the presence of an effective electromagnetic current which is generated by the momentum density of the matter/energy distribution, even for neutral sources. This implies that in the presence of dark energy, the motion of large-scale structures generates magnetic fields. Estimates of the present amplitude of the generated seed fields for typical spiral galaxies could reach $10^{-9}$ G without any amplification. In the case of compact rotating objects, the theory predicts their magnetic moments to be related to their angular momenta in the way suggested by the so called Schuster-Blackett conjecture.Comment: 5 pages, no figure

Certification of Bounds of Non-linear Functions: the Templates Method

The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of inequalities. We introduce an approximation algorithm, which combines ideas of the max-plus basis method (in optimal control) and of the linear templates method developed by Manna et al. (in static analysis). This algorithm consists in bounding some of the constituents of the function by suprema of quadratic forms with a well chosen curvature. This leads to semialgebraic optimization problems, solved by sum-of-squares relaxations. Templates limit the blow up of these relaxations at the price of coarsening the approximation. We illustrate the efficiency of our framework with various examples from the literature and discuss the interfacing with Coq.Comment: 16 pages, 3 figures, 2 table

Tensor products of subspace lattices and rank one density

We show that, if $M$ is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, $L$ is a commutative subspace lattice and $P$ is the lattice of all projections on a separable infinite dimensional Hilbert space, then the lattice $L\otimes M\otimes P$ is reflexive. If $M$ is moreover an atomic Boolean subspace lattice while $L$ is any subspace lattice, we provide a concrete lattice theoretic description of $L\otimes M$ in terms of projection valued functions defined on the set of atoms of $M$. As a consequence, we show that the Lattice Tensor Product Formula holds for \Alg M and any other reflexive operator algebra and give several further corollaries of these results.Comment: 15 page

Across the Indian Ocean: a remarkable example of trans-oceanic dispersal in an austral mygalomorph spider [dataset]

The Migidae are a family of austral trapdoor spiders known to show a highly restricted and disjunct distribution pattern. Here, we aim to investigate the phylogeny and historical biogeography of the group, which was previously thought to be vicariant in origin, and examine the biogeographic origins of the genus Moggridgea using a dated multi-gene phylogeny. Moggridgea specimens were sampled from southern Australia and Africa, and Bertmainus was sampled from Western Australia. Sanger sequencing methods were used to generate a robust six marker molecular dataset consisting of the nuclear genes 18S rRNA, 28S rRNA, ITS rRNA, XPNPEP3 and H3 and the mitochondrial gene COI. Bayesian and Maximum Likelihood methods were used to analyse the dataset, and the key dispersal nodes were dated using BEAST. Based on our data, we demonstrate that Moggridgea rainbowi from Kangaroo Island, Australia is a valid member of the otherwise African genus Moggridgea. Molecular clock dating analyses show that the inter-specific divergence of M. rainbowi from African congeners is between 2.27–16.02 million years ago (Mya). This divergence date significantly post-dates the separation of Africa from Gondwana (95 Mya) and therefore does not support a vicariant origin for Australian Moggridgea. It also pre-dates human colonisation of Kangaroo Island, a result which is further supported by the intra-specific divergence date of 1.10–6.39 Mya between separate populations on Kangaroo Island. These analyses provide strong support for the hypothesis that Moggridgea colonised Australia via long-distance trans-Indian Ocean dispersal, representing the first such documented case in a mygalomorph spider

Towards a formal description of the collapse approach to the inflationary origin of the seeds of cosmic structure

Inflation plays a central role in our current understanding of the universe. According to the standard viewpoint, the homogeneous and isotropic mode of the inflaton field drove an early phase of nearly exponential expansion of the universe, while the quantum fluctuations (uncertainties) of the other modes gave rise to the seeds of cosmic structure. However, if we accept that the accelerated expansion led the universe into an essentially homogeneous and isotropic space-time, with the state of all the matter fields in their vacuum (except for the zero mode of the inflaton field), we can not escape the conclusion that the state of the universe as a whole would remain always homogeneous and isotropic. It was recently proposed in [A. Perez, H. Sahlmann and D. Sudarsky, "On the quantum origin of the seeds of cosmic structure," Class. Quant. Grav. 23, 2317-2354 (2006)] that a collapse (representing physics beyond the established paradigm, and presumably associated with a quantum-gravity effect a la Penrose) of the state function of the inflaton field might be the missing element, and thus would be responsible for the emergence of the primordial inhomogeneities. Here we will discuss a formalism that relies strongly on quantum field theory on curved space-times, and within which we can implement a detailed description of such a process. The picture that emerges clarifies many aspects of the problem, and is conceptually quite transparent. Nonetheless, we will find that the results lead us to argue that the resulting picture is not fully compatible with a purely geometric description of space-time.Comment: 53 pages, no figures. Revision to match the published versio

Diffusion with rearranging traps

A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting polymers. In the present model the traps are infinite, unlike an earlier version with finite traps, this model has a percolation threshold. For the infinite trap version a simple analytical calculation is possible and the results agree qualitatively with simulation.Comment: Latex, five figure

Comparative study of density functional theories of the exchange-correlation hole and energy in silicon

We present a detailed study of the exchange-correlation hole and exchange-correlation energy per particle in the Si crystal as calculated by the Variational Monte Carlo method and predicted by various density functional models. Nonlocal density averaging methods prove to be successful in correcting severe errors in the local density approximation (LDA) at low densities where the density changes dramatically over the correlation length of the LDA hole, but fail to provide systematic improvements at higher densities where the effects of density inhomogeneity are more subtle. Exchange and correlation considered separately show a sensitivity to the nonlocal semiconductor crystal environment, particularly within the Si bond, which is not predicted by the nonlocal approaches based on density averaging. The exchange hole is well described by a bonding orbital picture, while the correlation hole has a significant component due to the polarization of the nearby bonds, which partially screens out the anisotropy in the exchange hole.Comment: 16 pages, 5 figures, RevTeX, added conten

Spin and charge ordering in self-doped Mott insulators

We have investigated possible spin and charge ordered states in 3d transition-metal oxides with small or negative charge-transfer energy, which can be regarded as self-doped Mott insulators, using Hartree-Fock calculations on d-p-type lattice models. It was found that an antiferromagnetic state with charge ordering in oxygen 2p orbitals is favored for relatively large charge-transfer energy and may be relevant for PrNiO$_3$ and NdNiO$_3$. On the other hand, an antiferromagnetic state with charge ordering in transition-metal 3$d$ orbitals tends to be stable for highly negative charge-transfer energy and can be stabilized by the breathing-type lattice distortion; this is probably realized in YNiO$_3$.Comment: 4 pages, 4 figure