Configuration mixing within the energy density functional formalism: pathologies and cures

Configuration mixing calculations performed in terms of the Skyrme/Gogny Energy Density Functional (EDF) rely on extending the Single-Reference energy functional into non-diagonal EDF kernels. The standard way to do so, based on an analogy with the pure Hamiltonian case and the use of the generalized Wick theorem, is responsible for the recently observed divergences and steps in Multi-Reference calculations. We summarize here the minimal solution to this problem recently proposed [Lacroix et al, arXiv:0809.2041] and applied with success to particle number restoration[Bender et al, arXiv:0809.2045]. Such a regularization method provides suitable corrections of pathologies for EDF depending on integer powers of the density. The specific case of fractional powers of the density[Duguet et al, arXiv:0809.2049] is also discussed.Comment: 5 pages, Proceedings of the French-Japanese Symposium, September 2008. To be published in Int. J. of Mod. Phys.

Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices

We discuss the origin of pathological behaviors that have been recently identified in particle-number-restoration calculations performed within the nuclear energy density functional framework. A regularization method that removes the problematic terms from the multi-reference energy density functional and which applies (i) to any symmetry restoration- and/or generator-coordinate-method-based configuration mixing calculation and (ii) to energy density functionals depending only on integer powers of the density matrices, was proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] and implemented for particle-number restoration calculations in [M. Bender, T. Duguet, D. Lacroix, arXiv:0809.2045]. In the present paper, we address the viability of non-integer powers of the density matrices in the nuclear energy density functional. Our discussion builds upon the analysis already carried out in [J. Dobaczewski \emph{et al.}, Phys. Rev. C \textbf{76}, 054315 (2007)]. First, we propose to reduce the pathological nature of terms depending on a non-integer power of the density matrices by regularizing the fraction that relates to the integer part of the exponent using the method proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]. Then, we discuss the spurious features brought about by the remaining fractional power. Finally, we conclude that non-integer powers of the density matrices are not viable and should be avoided in the first place when constructing nuclear energy density functionals that are eventually meant to be used in multi-reference calculations.Comment: 17 pages, 12 figures, accepted for publication in PR

An evaluation of Northern Florida Bay as a nursery area for red drum, Sciaenops ocellatus, and other juvenile and small resident fishes.

Red drum is one ofthe most popular species sought by anglers in Florida Bay, yet juveniles are rarely encountered. We evaluated Florida Bay as a nursery area for red drum by sampling for recently-settled late larvae in basin areas within the bay with an epi-benthic sled at six stations in November 2000, and at seven stations during December 2000 through February 2001. In November 2000 we surveyed potential sampling sites in quiet backwaters adjacent to mangroves for juvenile red drum. A total of 202 sites were sampled mainly in northern Florida Bay and adjacent waters with a cast net. We collected only one recently-settled red drum larvae and no juveniles. Obviously the sites that we sampled in Florida Bay and adjacent waters are not nursery habitat for this valuable species. Sled collections were dominated by bay anchovy, Anchoa mitchilli, but densities were biased by one collection. Five small resident species were among the dominant species: rainwater killifish, Lucania parva; dusky pipefish, Syngnathus floridae; dwarf seahorse, Hippocampus zosterae; and clown goby, Microgobius gulosus. Three species that spawn outside Florida Bay in the GulfofMexico were common: pinfish, Lagodon rhomboides; pigfish, Orthopristis chrysoptera; and silver perch, Bairdiella chrysoura. Twenty-seven species were collected with the cast net. Hardhead silversides (Atherinomorus stipes), bay anchovy, tidewater mojarra (Eucinostomus harengulus), silver jenny (Eucinostomus gula), and goldspotted killifish (Floridichthys carpio) were the most common in cast net collections. Although only one red drum was collected, we were able to: (1) identify mesohaline waters from our cast net sites to test our preliminary assessment that mesohaline habitat might be limited in Florida Bay, (2) document the distribution and abundance of fishes collected by cast net that should enhance our understanding of ichthyofauna in the Northern Subdivision ofFlorida Bay and adjacent waters, and (3) from epibenthic sled collections, describe the habitats, abundance and distribution of recently settled larvae/small juveniles/small resident fishes during late fall and winter. This information should be useful to managers and future research. (PDF contains 34 pages

Life History, Diet, Abundance and Distribution, and Length-Frequencies of Selected Invertebrates in Florida Bay, Everglades National Park, Florida

This report presents information on the life history, diet, abundance and distribution, and length-frequency distributions of five invertebrates in Florida Bay, Everglades National Park. Collections were made with an otter trawl in basins on a bi-monthly basis. Non-parametric statistics were used to test spatial and temporal differences in the abundance of invertebrates when numbers were appropriate (i. e., $25). Invertebrate species are presented in four sections. The sections on Life History, and Diet were derived from the literature. The section on Abundance and Distribution consists of data from otter-trawl collections. In addition, comparisons with other studies are included here following our results. The section on Length-frequency Distributions consists of length measurements from all collections, except 1984-1985 when no measurements were taken. Length-frequency distributions were used, when possible, to estimate life stage captured, spawning times, recruitment into Florida Bay for those species which spawn outside the Bay, and growth. Additional material from the literature was added when appropriate. (PDF contains 39 pages

A fiber-optic confocal scanner for scattering tissue

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 15, 2010).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Dissertation advisor: Dr. Mark A. Haidekker.Vita.Ph. D. University of Missouri--Columbia 2009.Confocal microscopy has become an important diagnostic tool in examining scattering tissues. The high resolution of confocal microscopy and its optical sectioning capabilities lend itself as a desirable modality in examining structures on the micrometer scale. While commercial confocal microscopes are readily available, they may not be suitable for examining tissues in vivo or able to accommodate large samples. The presented work offers a prototype device based on the principle of confocal microscopy that is versatile enough to be used not only as a small scale scanner, but adaptable for a wide range of situations. The automated capabilities of the scanner allow it to be used as a method of thickness measurement for tissue engineered cell sheets, in vivo examination of skin, and determining homogeneity in scattering tissues. The abilities and shortcomings of the device are investigated, and future adaptations of the device are proposed

Functional approach for pairing in finite systems: How to define restoration of broken symmetries in Energy Density Functional theory ?

The Multi-Reference Energy Density Functional (MR-EDF) approach (also called configuration mixing or Generator Coordinate Method), that is commonly used to treat pairing in finite nuclei and project onto particle number, is re-analyzed. It is shown that, under certain conditions, the MR-EDF energy can be interpreted as a functional of the one-body density matrix of the projected state with good particle number. Based on this observation, we propose a new approach, called Symmetry-Conserving EDF (SC-EDF), where the breaking and restoration of symmetry are accounted for simultaneously. We show, that such an approach is free from pathologies recently observed in MR-EDF and can be used with a large flexibility on the density dependence of the functional.Comment: proceeding of the conference "Many body correlations from dilute to dense Nuclear systems", Paris, February 201

Out of equilibrium transport through an Anderson impurity: Probing scaling laws within the equation of motion approach

We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T. Assuming that the interactions are taking place solely in the impurity and focusing in the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G_2(T,V) to test several scaling laws. We find that G_2(T,V)/G_2(T,0) is a universal function of both eV/T_K and T/T_K, being T_K the Kondo temperature. The effect of an in plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting \Delta, the computed differential conductance peak splitting depends only on \Delta/T_K, and for large fields approaches the value of 2\Delta . Besides the traditional two leads setup, we also consider other configurations that mimics recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as \ln(eV/T_K). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.Comment: 9 pages, 7 figure

Looking for ultralight dark matter near supermassive black holes

Measurements of the dynamical environment of supermassive black holes (SMBHs) are becoming abundant and precise. We use such measurements to look for ultralight dark matter (ULDM), which is predicted to form dense cores ("solitons") in the centre of galactic halos. We search for the gravitational imprint of an ULDM soliton on stellar orbits near Sgr A∗ and by combining stellar velocity measurements with Event Horizon Telescope imaging of M87∗. Finding no positive evidence, we set limits on the soliton mass for different values of the ULDM particle mass m. The constraints we derive exclude the solitons predicted by a naive extrapolation of the soliton-halo relation, found in DM-only numerical simulations, for 2×10-20 eV≲ m≲8×10-19 eV (from Sgr A∗) and m≲4×10-22 eV (from M87∗). However, we present theoretical arguments suggesting that an extrapolation of the soliton-halo relation may not be adequate: in some regions of the parameter space, the dynamical effect of the SMBH could cause this extrapolation to over-predict the soliton mass by orders of magnitude

Partial Disorder and Metal-Insulator Transition in the Periodic Anderson Model on a Triangular Lattice

Ground state of the periodic Anderson model on a triangular lattice is systematically investigated by the mean-field approximation. We found that the model exhibits two different types of partially disordered states: one is at half filling and the other is at other commensurate fillings. In the latter case, the kinetic energy is lowered by forming an extensive network involving both magnetic and nonmagnetic sites, in sharp contrast to the former case in which the nonmagnetic sites are rather isolated. This spatially extended nature of nonmagnetic sites yields a metallic partially-disordered state by hole doping. We discuss the mechanism of the metal-insulator transition by the change of electronic structure.Comment: 4 pages, 4 figures, accepted for publication in J. Phys. Soc. Jp

On nucleon exchange mechanism in heavy-ion collisions at near-barrier energies

Nucleon drift and diffusion mechanisms in central collisions of asymmetric heavy-ions at near-barrier energies are investigated in the framework of a stochastic mean-field approach. Expressions for diffusion and drift coefficients for nucleon transfer deduced from the stochastic mean-field approach in the semiclassical approximation have similar forms familiar from the phenomenological nucleon exchange model. The variance of fragment mass distribution agrees with the empirical formula $\sigma^2_{AA}(t)= N_{\rm exc}(t)$. The comparison with the time-dependent Hartree-Fock calculations shows that, below barrier energies, the drift coefficient in the semiclassical approximation underestimates the mean number of nucleon transfer obtained in the quantal framework. Motion of the window in the dinuclear system has a significant effect on the nucleon transfer in asymmetric collisions.Comment: 10 pages, 10 figures, submitted for publicatio