Construction of Wannier functions from localized atomic-like orbitals

The problem of construction of the Wannier functions (WFs) in a restricted Hilbert space of eigenstates of the one-electron Hamiltonian $\hat{H}$ (forming the so-called low-energy part of the spectrum) can be formulated in several different ways. One possibility is to use the projector-operator techniques, which pick up a set of trial atomic orbitals and project them onto the given Hilbert space. Another possibility is to employ the downfolding method, which eliminates the high-energy part of the spectrum and incorporates all related to it properties into the energy-dependence of an effective Hamiltonian. We show that by modifying the high-energy part of the spectrum of the original Hamiltonian $\hat{H}$, which is rather irrelevant to the construction of WFs in the low-energy part of the spectrum, these two methods can be formulated in an absolutely exact and identical form, so that the main difference between them is reduced to the choice of the trial orbitals. Concerning the latter part of the problem, we argue that an optimal choice for trial orbitals can be based on the maximization of the site-diagonal part of the density matrix. The main idea is illustrated for a simple toy model, consisting of only two bands, as well as for a more realistic example of $t_{2g}$ bands in V$_2$O$_3$. An analogy with the search of the ground state of a many-electron system is also discussed.Comment: 13 pages, 6 figure

First-principle Wannier functions and effective lattice fermion models for narrow-band compounds

We propose a systematic procedure for constructing effective lattice fermion models for narrow-band compounds on the basis of first-principles electronic structure calculations. The method is illustrated for the series of transition-metal (TM) oxides: SrVO$_3$, YTiO$_3$, V$_2$O$_3$, and Y$_2$Mo$_2$O$_7$. It consists of three parts, starting from LDA. (i) construction of the kinetic energy Hamiltonian using downfolding method. (ii) solution of an inverse problem and construction of the Wannier functions (WFs) for the given kinetic energy Hamiltonian. (iii) calculation of screened Coulomb interactions in the basis of \textit{auxiliary} WFs, for which the kinetic-energy term is set to be zero. The last step is necessary in order to avoid the double counting of the kinetic-energy term, which is included explicitly into the model. The screened Coulomb interactions are calculated in a hybrid scheme. First, we evaluate the screening caused by the change of occupation numbers and the relaxation of the LMTO basis functions, using the conventional constraint-LDA approach, where all matrix elements of hybridization involving the TM $d$ orbitals are set to be zero. Then, we switch on the hybridization and evaluate the screening associated with the change of this hybridization in RPA. The second channel of screening is very important, and results in a relatively small value of the effective Coulomb interaction for isolated $t_{2g}$ bands. We discuss details of this screening and consider its band-filling dependence, frequency dependence, influence of the lattice distortion, proximity of other bands, and the dimensionality of the model Hamiltonian.Comment: 35 pages, 25 figure

An Assessment of Grass Regeneration Nurseries at the Western Regional Plant Introduction Station, 1994-1997

The Western Regional Plant Introduction Station (WRPIS), Pullman, WA, USA, maintains over 17,000 accessions of forage and turf grasses that are mostly wind cross-pollinated and highly heterogenic. Regeneration procedures have been refined over the past nine years to include improved isolation distance and increased plant populations for regeneration. The grass regeneration nurseries planted from 1994 through 1997 were evaluated using data recorded in the Germplasm Resources Information Network (GRIN) and it was found that approximately 78% of the regenerations were successful. Reasons for failures were contributed to inadequate plant number, presence of disease, seed shattering, and unsuitable growing environment. Several solutions have been identified and implemented

Conservation of Grass Collections at the Western Regional Plant Introduction Station

Germplasm managers at the Western Regional Plant Introduction Station (WRPIS) have focused on improving seed regeneration in forage and turf grass species through studies of diversity maintenance, using isozyme markers in annual ryegrass (Lolium multiflorum Lam.) and through studies of pollen isolation, using strains of dominant pubescent and recessive glabrous smooth bromegrass (Bromus inermis Leyss.). Balanced samples of annual ryegrass (an equal number of seeds per plant) from field plots were best for maintaining allelic frequencies, but genetic diversity (heterozygosity and allelic richness) was maintained nearly as well in bulk samples (seeds proportionally assembled according to seeds per plant) during early regeneration cycles. In 1995, bromegrass marker plots integrated into WRPIS seed-regeneration nurseries at two locations resulted in average contamination of 4.2% at distances between 22 and 27 m. Diversity maintenance in early regeneration cycles and a relatively low level of pollen contamination appear possible in bulk samples and with modest isolation distances

Explosion of a collapsing Bose-Einstein condensate

We show that elastic collisions between atoms in a Bose-Einstein condensate with attractive interactions lead to an explosion that ejects a large fraction of the collapsing condensate. We study variationally the dynamics of this explosion and find excellent agreement with recent experiments on magnetically trapped Rubidium-85. We also determine the energy and angular distribution of the ejected atoms during the collapse.Comment: Four pages of ReVTeX and five postscript figure

The Surface of a Bose-Einstein Condensed Atomic Cloud

We investigate the structure and collective modes of a planar surface of a trapped Bose-Einstein condensed gas at zero temperature. In the long-wavelength limit we find a mode similar to the gravity wave on the surface of a fluid with the frequency $\omega$ and the wavenumber $q$ related by $\omega^2=Fq/m$. Here $F$ is the force due to the confining potential at the surface and $m$ is the particle mass. At shorter wavelengths we use a variational approach and find corrections to $\omega^2$ of order $q^4 \ln{q}$. We demonstrate the usefulness of the concept of an effective surface tension for describing both static and dynamic properties of condensed atomic clouds.Comment: 8 pages, REVTEX, submitted to Phys. Rev.

Fingerprints of Spin-Orbital Physics in Crystalline O2_2

The alkali hyperoxide KO$_2$ is a molecular analog of strongly-correlated systems, comprising of orbitally degenerate magnetic O$_2^-$ ions. Using first-principles electronic structure calculations, we set up an effective spin-orbital model for the low-energy \textit{molecular} orbitals and argue that many anomalous properties of KO$_2$ replicate the status of its orbital system in various temperature regimes.Comment: 4 pages, 2 figures, 1 tabl

Initial Stages of Bose-Einstein Condensation

We present the quantum theory for the nucleation of Bose-Einstein condensation in a dilute atomic Bose gas. This quantum theory comfirms the results of the semiclassical treatment, but has the important advantage that both the kinetic and coherent stages of the nucleation process can now be described in a unified way by a single Fokker-Planck equation.Comment: Four pages of ReVTeX and no figure

Recovery of critically endangered Nassau grouper (Epinephelus striatus) in the Cayman Islands following targeted conservation actions.

Many large-bodied marine fishes that form spawning aggregations, such as the Nassau grouper (Epinephelus striatus), have suffered regional overfishing due to exploitation during spawning. In response, marine resource managers in many locations have established marine protected areas or seasonal closures to recover these overfished stocks. The challenge in assessing management effectiveness lies largely in the development of accurate estimates to track stock size through time. For the past 15 y, the Cayman Islands government has taken a series of management actions aimed at recovering collapsed stocks of Nassau grouper. Importantly, the government also partnered with academic and nonprofit organizations to establish a research and monitoring program (Grouper Moon) aimed at documenting the impacts of conservation action. Here, we develop an integrated population model of 2 Cayman Nassau grouper stocks based on both diver-collected mark-resight observations and video censuses. Using both data types across multiple years, we fit parameters for a state-space model for population growth. We show that over the last 15 y the Nassau grouper population on Little Cayman has more than tripled in response to conservation efforts. Census data from Cayman Brac, while more sparse, show a similar pattern. These findings demonstrate that spatial and seasonal closures aimed at rebuilding aggregation-based fisheries can foster conservation success