Quantum Mechanics on SO(3) via Non-commutative Dual Variables

We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the non-commutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the non-trivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semi-classical approximation of the first order path integral and the example of a free particle on SO(3). On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam models.Comment: 29 pages; matches the published version plus footnote 7, a journal reference include

Learning Incoherent Subspaces: Classification via Incoherent Dictionary Learning

In this article we present the supervised iterative projections and rotations (s-ipr) algorithm, a method for learning discriminative incoherent subspaces from data. We derive s-ipr as a supervised extension of our previously proposed iterative projections and rotations (ipr) algorithm for incoherent dictionary learning, and we employ it to learn incoherent sub-spaces that model signals belonging to different classes. We test our method as a feature transform for supervised classification, first by visualising transformed features from a synthetic dataset and from the ‘iris’ dataset, then by using the resulting features in a classification experiment

Muon and Tau Neutrinos Spectra from Solar Flares

Solar neutrino flares and mixing are considered. Most power-full solar flare as the ones occurred on 23th February 1956, September 29th 1989, 28th October and on 2nd-4th November 2003 are sources of cosmic rays, X, gamma and neutrino bursts. These flares took place both on front or in the edge and in the hidden solar disk. The observed and estimated total flare energy should be a source of a prompt secondary neutrino burst originated, by proton-proton-pion production on the sun itself; a more delayed and spread neutrino flux signal arise by the solar charged flare particles reaching the terrestrial atmosphere. Our first estimates of neutrino signals in largest underground detectors hint for few events in correlation with, gamma,radio onser. Our approximated spectra for muons and taus from these rare solar eruption are shown over the most common background. The muon and tau signature is very peculiar and characteristic over electron and anti-electron neutrino fluxes. The rise of muon neutrinos will be detectable above the minimal muon threshold of 113 MeV. The rarest tau appearence will be possible only for hardest solar neutrino energies above 3.471 GeVComment: 14 pages, 4 figures, Vulcano Conference 200

Raman scattering from phonons and magnons in RFe3)BO3)4

Inelastic light scattering spectra of several members of the RFe3(BO3)4 family reveal a cascade of phase transitions as a function of temperature, starting with a structural, weakly first order, phase transition followed by two magnetic phase transitions. Those consist of the ordering of the Fe-spin sublattice revealed by all the compound, and a subsequent spin-reorientational transition for GdFe3(BO3)4. The Raman data evidence a strong coupling between the lattice and magnetic degrees of freedom in these borates. The Fe-sublattice ordering leads to a strong suppression of the low energy magnetic scattering, and a multiple peaked two-magnon scattering continuum is observed. Evidence for short-range correlations is found in the `paramagnetic' phase by the observation of a broad magnetic continuum in the Raman data, which persists up to surprisingly high temperatures.Comment: 17 pages, 13 figure

Wave Mechanics of a Two Wire Atomic Beamsplitter

We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to non-adiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three dimensional structure of the beam splitter, gathering quantitative information about mode-mixing, splitting ratios,and reflection and transmission probabilities

Extrafloral-nectar based partner manipulation in plant-ant relationship

Plant–ant interactions are generally considered as mutualisms, with both parties gaining benefits from the association. It has recently emerged that some of these mutualistic associations have, however, evolved towards other forms of relationships and, in particular, that plants may manipulate their partner ants to make reciprocation more beneficial, thereby stabilizing the mutualism. Focusing on plants bearing extrafloral nectaries, we review recent studies and address three key questions: (i) how can plants attract potential partners and maintain their services; (ii) are there compounds in extrafloral nectar that could mediate partner manipulation; and (iii) are ants susceptible to such compounds? After reviewing the current knowledge on plant–ant associations, we propose a possible scenario where plant-derived chemicals, such as secondary metabolites, known to have an impact on animal brain, could have evolved in plants to attract and manipulate ant behaviour. This new viewpoint would place plant–animal interaction in a different ecological context, opening new ecological and neurobiological perspectives of drug seeking and use

Pinch Technique for Schwinger-Dyson equations

In the context of scalar QED we derive the pinch technique self-energies and vertices directly from the Schwinger-Dyson equations. After reviewing the perturbative construction, we discuss in detail the general methodology and the basic field-theoretic ingredients necessary for the completion of this task. The construction requires the simultaneous treatment of the equations governing the scalar self-energy and the fundamental interaction vertices. The resulting non-trivial rearrangement of terms generates dynamically the Schwinger-Dyson equations for the corresponding Green's functions of the background field method. The proof relies on the extensive use of the all-order Ward-identities satisfied by the full vertices of the theory and by the one-particle-irreducible kernels appearing in the usual skeleton expansion. The Ward identities for these latter quantities are derived formally, and several subtleties related to the structure of the multiparticle kernels are addressed. The general strategy for the generalization of the method in a non-Abelian context is briefly outlined, and some of the technical difficulties are discussed.Comment: 43 pages, 11 figures; title and abstract slightly modified, several clarifying discussions added; final version to match the one accpted for publication in JHE

Beyond the plane-parallel and Newtonian approach: Wide-angle redshift distortions and convergence in general relativity

We extend previous analyses of wide-angle correlations in the galaxy power spectrum in redshift space to include all general relativistic effects. These general relativistic corrections to the standard approach become important on large scales and at high redshifts, and they lead to new terms in the wide-angle correlations. We show that in principle the new terms can produce corrections of nearly 10 % on Gpc scales over the usual Newtonian approximation. General relativistic corrections will be important for future large-volume surveys such as SKA and Euclid, although the problem of cosmic variance will present a challenge in observing this.Comment: 14 pages, 5 figures; Typo in equation 5 corrected; results unaffecte