Closed-form expressions for correlated density matrices: application to dispersive interactions and example of (He)2

Empirically correlated density matrices of N-electron systems are investigated. Exact closed-form expressions are derived for the one- and two-electron reduced density matrices from a general pairwise correlated wave function. Approximate expressions are proposed which reflect dispersive interactions between closed-shell centro-symmetric subsystems. Said expressions clearly illustrate the consequences of second-order correlation effects on the reduced density matrices. Application is made to a simple example: the (He)2 system. Reduced density matrices are explicitly calculated, correct to second order in correlation, and compared with approximations of independent electrons and independent electron pairs. The models proposed allow for variational calculations of interaction energies and equilibrium distance as well as a clear interpretation of dispersive effects on electron distributions. Both exchange and second order correlation effects are shown to play a critical role on the quality of the results.Comment: 22 page

Non-resonant pitch-angle scattering, and parallel mean-free-path

Abstract A new, non-resonant pitch-angle scattering process has been found, which very efficiently scatters the cosmic ray particles through the zero pitch-angle cosine. Combined with the effects of gyroresonance and transit-time damping, it can solve the "flatness problem" for the parallel mean-free-path as a function of the particles rigidity. The main lines of its derivation, and the implications on the mean-free-path at low rigidities ( ¢ ¡ ¤ £ ¦ ¥ MV), are summarized here

Fourier-Legendre expansion of the one-electron density-matrix of ground-state two-electron atoms

The density-matrix rho(r, r') of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials Pl(cos(theta) = r.r'/rr'). Application is here made to harmonically trapped electron pairs (i.e. Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r, r'). The series expansions are shown to converge rapidly in each case, with respect to both the electron number and the kinetic energy. In practice, a two-term expansion accounts for most of the correlation effects, so that the correlated density-matrices of the atoms at issue are essentially a linear functions of P1(cos(theta)) = cos(theta). For example, in the case of the Hooke's atom: a two-term expansion takes in 99.9 % of the electrons and 99.6 % of the kinetic energy. The correlated density-matrices obtained are finally compared to their determinantal counterparts, using a simplified representation of the density-matrix rho(r, r'), suggested by the Legendre expansion. Interestingly, two-particle correlation is shown to impact the angular delocalization of each electron, in the one-particle space spanned by the r and r' variables.Comment: 31 pages, 7 figure

Exact Kohn-Sham versus Hartree-Fock in momentum-space: examples of two-fermion systems

The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentum space studies. The systems considered are the Moshinsky atom, the Hooke's atom and light two-electron ions, for which expressions for correlated density-matrices or momentum densities have been derived in closed-form. The results obtained show that it is necessary to make a distinction between true and approximate DFT.Comment: 30 pages, accepted for publication in J. Chem. Phys. (2006

Angular versus radial correlation effects on momentum distributions of light two-electron ions

We investigate different correlation mechanisms for two-electron systems and compare their respective effects on various electron distributions. The simplicity of the wave functions used allows for the derivation of closed-form analytical expressions for all electron distributions. Among other features, it is shown that angular and radial correlation mechanisms have opposite effects on Compton profiles at small momenta.Comment: 22 pages, 5 figures, 3 tabl

The large longitudinal spread of solar energetic particles during the January 17, 2010 solar event

We investigate multi-spacecraft observations of the January 17, 2010 solar energetic particle event. Energetic electrons and protons have been observed over a remarkable large longitudinal range at the two STEREO spacecraft and SOHO suggesting a longitudinal spread of nearly 360 degrees at 1AU. The flaring active region, which was on the backside of the Sun as seen from Earth, was separated by more than 100 degrees in longitude from the magnetic footpoints of each of the three spacecraft. The event is characterized by strongly delayed energetic particle onsets with respect to the flare and only small or no anisotropies in the intensity measurements at all three locations. The presence of a coronal shock is evidenced by the observation of a type II radio burst from the Earth and STEREO B. In order to describe the observations in terms of particle transport in the interplanetary medium, including perpendicular diffusion, a 1D model describing the propagation along a magnetic field line (model 1) (Dr\"oge, 2003) and the 3D propagation model (model 2) by (Dr\"oge et al., 2010) including perpendicular diffusion in the interplanetary medium have been applied, respectively. While both models are capable of reproducing the observations, model 1 requires injection functions at the Sun of several hours. Model 2, which includes lateral transport in the solar wind, reveals high values for the ratio of perpendicular to parallel diffusion. Because we do not find evidence for unusual long injection functions at the Sun we favor a scenario with strong perpendicular transport in the interplanetary medium as explanation for the observations.Comment: The final publication is available at http://www.springerlink.co

Evidence for Nearby Supernova Explosions

Supernova explosions are one of the most energetic--and potentially lethal--phenomena in the Universe. Scientists have speculated for decades about the possible consequences for life on Earth of a nearby supernova, but plausible candidates for such an event were lacking. Here we show that the Scorpius-Centaurus OB association, a group of young stars currently located at~130 parsecs from the Sun, has generated 20 SN explosions during the last 11 Myr, some of them probably as close as 40 pc to our planet. We find that the deposition on Earth of 60Fe atoms produced by these explosions can explain the recent measurements of an excess of this isotope in deep ocean crust samples. We propose that ~2 Myr ago, one of the SNe exploded close enough to Earth to seriously damage the ozone layer, provoking or contributing to the Pliocene-Pleistocene boundary marine extinction.Comment: 4 pages, 2 figures. Replaced by final version to appear in Physical Review Letter

The GCP molecular marker toolkit, an instrument for use in breeding food security crops

Crop genetic resources carry variation useful for overcoming the challenges of modern agriculture. Molecular markers can facilitate the selection of agronomically important traits. The pervasiveness of genomics research has led to an overwhelming number of publications and databases, which are, nevertheless, scattered and hence often difficult for plant breeders to access, particularly those in developing countries. This situation separates them from developed countries, which have better endowed programs for developing varieties. To close this growing knowledge gap, we conducted an intensive literature review and consulted with more than 150 crop experts on the use of molecular markers in the breeding program of 19 food security crops. The result was a list of effectively used and highly reproducible sequence tagged site (STS), simple sequence repeat (SSR), single nucleotide polymorphism (SNP), and sequence characterized amplified region (SCAR) markers. However, only 12 food crops had molecular markers suitable for improvement. That is, marker-assisted selection is not yet used for Musa spp., coconut, lentils, millets, pigeonpea, sweet potato, and yam. For the other 12 crops, 214 molecular markers were found to be effectively used in association with 74 different traits. Results were compiled as the GCP Molecular Marker Toolkit, a free online tool that aims to promote the adoption of molecular approaches in breeding activities

Insights on the Neuromagnetic Representation of Temporal Asymmetry in Human Auditory Cortex.

Communication sounds are typically asymmetric in time and human listeners are highly sensitive to this short-term temporal asymmetry. Nevertheless, causal neurophysiological correlates of auditory perceptual asymmetry remain largely elusive to our current analyses and models. Auditory modelling and animal electrophysiological recordings suggest that perceptual asymmetry results from the presence of multiple time scales of temporal integration, central to the auditory periphery. To test this hypothesis we recorded auditory evoked fields (AEF) elicited by asymmetric sounds in humans. We found a strong correlation between perceived tonal salience of ramped and damped sinusoids and the AEFs, as quantified by the amplitude of the N100m dynamics. The N100m amplitude increased with stimulus half-life time, showing a maximum difference between the ramped and damped stimulus for a modulation half-life time of 4 ms which is greatly reduced at 0.5 ms and 32 ms. This behaviour of the N100m closely parallels psychophysical data in a manner that: i) longer half-life times are associated with a stronger tonal percept, and ii) perceptual differences between damped and ramped are maximal at 4 ms half-life time. Interestingly, differences in evoked fields were significantly stronger in the right hemisphere, indicating some degree of hemispheric specialisation. Furthermore, the N100m magnitude was successfully explained by a pitch perception model using multiple scales of temporal integration of auditory nerve activity patterns. This striking correlation between AEFs, perception, and model predictions suggests that the physiological mechanisms involved in the processing of pitch evoked by temporal asymmetric sounds are reflected in the N100m