Multipole expansion

About: Multipole expansion is a research topic. Over the lifetime, 9675 publications have been published within this topic receiving 214783 citations.

Coupled Quintessence

Abstract: A new component of the cosmic medium, a light scalar field or ''quintessence '', has been proposed recently to explain cosmic acceleration with a dynamical cosmological constant Such a field is expected to be coupled explicitely to ordinary matter, unless some unknown symmetry prevents it I investigate the cosmological consequences of such a coupled quintessence (CQ) model, assuming an exponential potential and a linear coupling This model is conformally equivalent to Brans-Dicke Lagrangians with power-law potential I evaluate the density perturbations on the cosmic microwave background and on the galaxy distribution at the present and derive bounds on the coupling constant from the comparison with observational data A novel feature of CQ is that during the matter dominated era the scalar field has a finite and almost constant energy density This epoch, denoted as $\phi $MDE, is responsible of several differences with respect to uncoupled quintessence: the multipole spectrum of the microwave background is tilted at large angles, the acoustic peaks are shifted, their amplitude is changed, and the present 8Mpc$/h$ density variance is diminished The present data constrain the dimensionless coupling constant to $|\beta |\leq 01$

Testing aspherical atom refinements on small-molecule data sets

Abstract: X-ray data on silicon, tetracyanoethylene, p-nitropyridine N-oxide and ammonium thiocyanate are refined with a generalized aspherical-atom formalism as introduced by Stewart, but modified to have a spherical valence more similar to the unperturbed HF valence shell. Several types of radial dependences of the multipole functions are tested and criteria are developed for judging the adequacy of the aspherical-atom refinement. The aspherical-atom model leads to a significant decrease in the least-squares error function, a reduction of features in the residual map, and an improvement in thermal parameters when comparison is made with the neutron results or when the rigid-bond postulate proposed by Hirshfeld is applied. Positional parameters are often improved except in the case of terminal atoms for which discrepancies, attributed to correlation between dipole-population and positional parameters, are sometimes observed. Deformation maps based on the aspherical-atom least-squares parameters contain less noise than X -- N maps and benefit from inclusion of calculated values of weak structure amplitudes in the summation. In the cases studied, deformation maps including terms beyond the experimental resolution do not yield additional information.

GFN2-xTB-An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions.

Abstract: An extended semiempirical tight-binding model is presented, which is primarily designed for the fast calculation of structures and noncovalent interaction energies for molecular systems with roughly 1000 atoms. The essential novelty in this so-called GFN2-xTB method is the inclusion of anisotropic second order density fluctuation effects via short-range damped interactions of cumulative atomic multipole moments. Without noticeable increase in the computational demands, this results in a less empirical and overall more physically sound method, which does not require any classical halogen or hydrogen bonding corrections and which relies solely on global and element-specific parameters (available up to radon, Z = 86). Moreover, the atomic partial charge dependent D4 London dispersion model is incorporated self-consistently, which can be naturally obtained in a tight-binding picture from second order density fluctuations. Fully analytical and numerically precise gradients (nuclear forces) are implemented. The...

Quantized electric multipole insulators

Abstract: The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.