Pairing correlations beyond the mean field

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys. E, in prin

The Significance of Micas in Ancient Cross-bedded Sandstones

In our study of thin sections of the cross-bedded Coconino Sandstone we encountered muscovite as a trace mineral in almost every thin section of the hundreds that we cut. As we began to study other similar cross-bedded sandstones like the Tensleep, Lyons and Hopeman the same pattern began to emerge. All of these sandstones have been conventionally interpreted as desert wind-blown deposits. A novel set of experiments were performed and recently published by some Cedarville University geology students and the lead author of this paper (Anderson et al., 2017). They found when muscovite-rich quartz sand was experimentally placed into a simulated eolian setting, muscovite only survived for a matter of days. When muscovite-rich quartz sand was experimentally placed into a simulated subaqueous setting it was still present after a year of constant agitation before the experiment was finally terminated. Even though this was a simple experiment and only a limited number of trials were performed it confirms field observations by the authors that mica is rare in modern eolian deposits (unless they are very near a granitic source) and its relative abundance in beach and marine sands. The implications are significant. Although more experiments could be performed, the experiments and observations suggest that mica is rapidly degraded in wind-blown environments and survives when transported by water. Evidently water cushions the grain-to-grain collisions and prevents rapid deterioration of the muscovite in subaqueous settings. This proposed paper will catalog and illustrate the large number of cross-bedded sandstones we have found that contain mica (mostly muscovite) as an accessory mineral. The dominant conventional view is that these sandstones are eolian, but the presence of muscovite based on experimental data and field observations suggests otherwise. The presence of muscovite in cross-bedded sandstones can be used as one of many criteria to argue for subaqueous deposition

Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory

The density of an atom in a state of well-defined angular momentum has a specific finite spherical harmonic content, without and with interactions. Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and Local Density Approximations, generally violate this feature. We analyze, by means of perturbation theory, the degree of this violation and show that it is small. The correct symmetry of the density can be assured by a constrained-search formulation without significantly altering the calculated energies. We compare our procedure to the (different) common practice of spherically averaging the self-consistent potential. Kohn-Sham density functional theory with the exact exchange-correlation potential has the correct finite spherical harmonic content in its density; but the corresponding exact single particle potential and wavefunctions contain an infinite number of spherical harmonics.Comment: 11 pages, 6 figures. Expanded discussion of spherical harmonic expansion of Hartree density. Some typos corrected, references adde

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 evolution operator of the Hartree-type equation with a quadratic potential

Based on the ideology of the Maslov's complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov-Anandan geometric phases are found in explicit form for the quasi-energy states.Comment: 23 pege

Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 13 pages, no figure

Quantum versus classical statistical dynamics of an ultracold Bose gas

We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and Hartree-Fock-Bogoliubov mean-field theories, which can be obtained as classical (statistical) field-theory approximations of the quantum many-body problem. We employ functional-integral techniques based on the two-particle irreducible (2PI) effective action. The role of quantum fluctuations is studied within the nonperturbative 2PI 1/N expansion to next-to-leading order. At this accuracy level memory-integrals enter the dynamic equations, which differ for quantum and classical statistical descriptions. This can be used to obtain a 'classicality' condition for the many-body dynamics. We exemplify this condition by studying the nonequilibrium evolution of a 1D Bose gas of sodium atoms, and discuss some distinctive properties of quantum versus classical statistical dynamics.Comment: 19 pages, 10 figure

A new purple sulfur bacterium from saline littoral sediments, Thiorhodotvibrio winogradskyi gen. nov. and sp. nov.

Two strains of a new purple sulfur bacterium were isolated in pure culture from the littoral sediment of a saline lake (Mahoney Lake, Canada) and a marine microbial mat from the North Sea island of Mellum, respectively. Single cells were vibrioid-to spirilloid-shaped and motile by means of single polar flagella. Intracellular photosynthetic membranes were of the vesicular type. As photosynthetic pigments, bacteriochlorophyll a and the carotenoids lycopene, rhodopin, anhydrorhodovibrin, rhodovibrin and spirilloxanthin were present. Hydrogen sulfide and elemental sulfur were used under anoxic conditions for phototrophic growth. In addition one strain (06511) used thiosulfate. Carbon dioxide, acetate and pyruvate were utilized by both strains as carbon sources. Depending on the strain propionate, succinate, fumarate, malate, tartrate, malonate, glycerol or peptone may additionally serve as carbon sources in the light. Optimum growth rates were obtained at pH 7.2, 33 °C, 50 mol m-2 s-1 intensity of daylight fluorescent tubes and a salinity of 2.2–3.2% NaCl. During growth on sulfide, up to ten small sulfur globules were formed inside the cells. The strains grew microaerophilic in the dark and exhibited high specific respiration rates. No vitamins were required for growth. The DNA base composition was 61.0–62.4 mol% G+C. The newly isolated bacterium belongs to the family chromatiaceae and is described as a member of a new genus and species, Thiorhodovibrio winogradskyi gen. nov. and sp. nov. with the type strain SSP1, DSM No. 6702

Non-Linear Vibrations in Nuclei

We have perfomed Time Dependant Hartree-Fock (TDHF) calculations on the non linear response of nuclei. We have shown that quadrupole (and dipole) motion produces monopole (and quadrupole) oscillations in all atomic nuclei. We have shown that these findings can be interpreted as a large coupling between one and two phonon states leading to large anharmonicities.Comment: 4 pages, 3 figure

Hydrogen and Helium atoms in strong magnetic fields

The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.Comment: 15 pages, 6 figure