From Microscales to Macroscales in 3D: Selfconsistent Equation of State for Supernova and Neutron Star Models

First results from a fully self-consistent, temperature-dependent equation of state that spans the whole density range of neutron stars and supernova cores are presented. The equation of state (EoS) is calculated using a mean-field Hartree-Fock method in three dimensions (3D). The nuclear interaction is represented by the phenomenological Skyrme model in this work, but the EoS can be obtained in our framework for any suitable form of the nucleon-nucleon effective interaction. The scheme we employ naturally allows effects such as (i) neutron drip, which results in an external neutron gas, (ii) the variety of exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii) the subsequent dissolution of these nuclei into nuclear matter. In this way, the equation of state is calculated across phase transitions without recourse to interpolation techniques between density regimes described by different physical models. EoS tables are calculated in the wide range of densities, temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000 processors simultaneously.Comment: 6 pages, 11 figures. Published in conference proceedings Journal of Physics: Conference Series 46 (2006) 408. Extended version to be submitted to Phys. Rev.

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

Theory and simulation of ultra-high-temperature ceramics

At Imperial College our group contributes theory and simulation advances to the Materials for Extreme Environments (XMat) project. Our research supports experiment and industry by developing and applying new high-temperature modelling techniques. These techniques are broad-ranging, from CALPHAD and DFT, to interatomic potentials and analytic models. Here we present advances on each approach and re-cover highlights including: - the release of MEAMfit, the interatomic potential fitting code - the development of the TU-TILD approach, for fast and full-order anharmonic thermodynamics [1] - a new first-principles-assisted CALPHAD assessment of ZrC - analytic models of strain and anharmonicity in carbides and borides - ab initio prediction of intrinsic defects at ultra-high temperatures - first principles heat and charge transport predictions for carbides Further, we summarise ongoing developments from the theory and simulation group, such as on first principles MAX phase thermodynamics Please click Additional Files below to see the full abstract

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

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

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

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

Optimal use of time dependent probability density data to extract potential energy surfaces

A novel algorithm was recently presented to utilize emerging time dependent probability density data to extract molecular potential energy surfaces. This paper builds on the previous work and seeks to enhance the capabilities of the extraction algorithm: An improved method of removing the generally ill-posed nature of the inverse problem is introduced via an extended Tikhonov regularization and methods for choosing the optimal regularization parameters are discussed. Several ways to incorporate multiple data sets are investigated, including the means to optimally combine data from many experiments exploring different portions of the potential. Results are presented on the stability of the inversion procedure, including the optimal combination scheme, under the influence of data noise. The method is applied to the simulated inversion of a double well system.Comment: 34 pages, 5 figures, LaTeX with REVTeX and Graphicx-Package; submitted to PhysRevA; several descriptions and explanations extended in Sec. I

Formation and control of electron molecules in artificial atoms: Impurity and magnetic-field effects

Interelectron interactions and correlations in quantum dots can lead to spontaneous symmetry breaking of the self-consistent mean field resulting in formation of Wigner molecules. With the use of spin-and-space unrestricted Hartree-Fock (sS-UHF) calculations, such symmetry breaking is discussed for field-free conditions, as well as under the influence of an external magnetic field. Using as paradigms impurity-doped (as well as the limiting case of clean) two-electron quantum dots (which are analogs to helium-like atoms), it is shown that the interplay between the interelectron repulsion and the electronic zero-point kinetic energy leads, for a broad range of impurity parameters, to formation of a singlet ground-state electron molecule, reminiscent of the molecular picture of doubly-excited helium. Comparative analysis of the conditional probability distributions for the sS-UHF and the exact solutions for the ground state of two interacting electrons in a clean parabolic quantum dot reveals that both of them describe formation of an electron molecule with similar characteristics. The self-consistent field associated with the triplet excited state of the two-electron quantum dot (clean as well as impurity-doped) exhibits symmetry breaking of the Jahn-Teller type, similar to that underlying formation of nonspherical open-shell nuclei and metal clusters. Furthermore, impurity and/or magnetic-field effects can be used to achieve controlled manipulation of the formation and pinning of the discrete orientations of the Wigner molecules. Impurity effects are futher illustrated for the case of a quantum dot with more than two electrons.Comment: Latex/Revtex, 10 pages with 4 gif figures. Small changes to explain the difference between Wigner and Jahn-Teller electron molecules. A complete version of the paper with high quality figures inside the text is available at http://shale.physics.gatech.edu/~costas/qdhelium.html For related papers, see http://www.prism.gatech.edu/~ph274c

Majorana solutions to the two-electron problem

A review of the known different methods and results devised to study the two-electron atom problem, appeared in the early years of quantum mechanics, is given, with particular reference to the calculations of the ground state energy of helium. This is supplemented by several, unpublished results obtained around the same years by Ettore Majorana, which results did not convey in his published papers on the argument, and thus remained unknown until now. Particularly interesting, even for current research in atomic and nuclear physics, is a general variant of the variational method, developed by Majorana in order to take directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Moreover, notable calculations specialized to the study of the two-electron problem show the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results), and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable, contributions to the ground state energy of an atom with given Z coming also from any other Z. Instead, contributions relevant mainly for pedagogical reasons count simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as a simple alternative to Hylleraas' method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure