Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies

A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with $s,p,d$ one-particle orbitals is presented. We find exact nodes for some cases of two electron atomic and molecular states and also the first exact node for the three-electron atomic system in $^4S(p^3)$ state using appropriate coordinate maps and wavefunction symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into 3D space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wavefunctions.Comment: 7 pages, 7 figure

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig

Optical absorption in boron clusters B6_{6} and B6+_{6}^{+} : A first principles configuration interaction approach

The linear optical absorption spectra in neutral boron cluster B$_{6}$ and cationic B$_{6}^{+}$ are calculated using a first principles correlated electron approach. The geometries of several low-lying isomers of these clusters were optimized at the coupled-cluster singles doubles (CCSD) level of theory. With these optimized ground-state geometries, excited states of different isomers were computed using the singles configuration-interaction (SCI) approach. The many body wavefunctions of various excited states have been analysed and the nature of optical excitation involved are found to be of collective, plasmonic type.Comment: 22 pages, 38 figures. An invited article submitted to European Physical Journal D. This work was presented in the International Symposium on Small Particles and Inorganic Clusters - XVI, held in Leuven, Belgiu

Optimization of inhomogeneous electron correlation factors in periodic solids

A method is presented for the optimization of one-body and inhomogeneous two-body terms in correlated electronic wave functions of Jastrow-Slater type. The most general form of inhomogeneous correlation term which is compatible with crystal symmetry is used and the energy is minimized with respect to all parameters using a rapidly convergent iterative approach, based on Monte Carlo sampling of the energy and fitting energy fluctuations. The energy minimization is performed exactly within statistical sampling error for the energy derivatives and the resulting one- and two-body terms of the wave function are found to be well-determined. The largest calculations performed require the optimization of over 3000 parameters. The inhomogeneous two-electron correlation terms are calculated for diamond and rhombohedral graphite. The optimal terms in diamond are found to be approximately homogeneous and isotropic over all ranges of electron separation, but exhibit some inhomogeneity at short- and intermediate-range, whereas those in graphite are found to be homogeneous at short-range, but inhomogeneous and anisotropic at intermediate- and long-range electron separation.Comment: 23 pages, 15 figures, 1 table, REVTeX4, submitted to PR

Building resilience to stress through leisure activities : a qualitative analysis

Stress is prevalent in modern society and coping strategies largely determine well-being. A qualitative investigation of leisure as a positive coping response to stress was undertaken using a resilience-based perspective. This approach enabled a focus on competencies and strengths in the stress-leisure-coping process, contributing to the sparse literature in this area. In-depth interviews were conducted with a sample of eight participants. From a thematic analysis three overall themes emerged: leisure as a buffer of stress, the relationship between negative and positive emotions and leisure, and benefits of leisure for coping with stress. The findings demonstrate how leisure facilitates a sense of resilience and its preventative functions. The results are discussed in relation to relevant theoretical propositions concerning the role of positive emotion in coping. In particular, the broaden-and-build theory provided a meaningful framework for suggesting how leisure and positive emotions acted in tandem to develop psychosocial resources over time

The role of electronic correlation in the Si(100) reconstruction: a quantum Monte Carlo study

Recent low-temperature scanning tunneling experiments have challenged the generally accepted picture of buckled silicon dimers as the ground state reconstruction of the Si(100) surface. Together with the symmetric dimer model of the surface suggested by quantum chemistry calculations on small clusters, these findings question our general understanding of electronic correlations at surfaces and its proper description within density functional theory. We present quantum Monte Carlo calculations on large cluster models of the symmetric and buckled surface, and conclude that buckling remains energetically more favorable even when the present-day best treatment of electronic correlation is employed.Comment: 5 pages, Revtex, 10 figure

Prostate-Specific Ets (PSE) factor: a novel marker for detection of metastatic breast cancer in axillary lymph nodes

Prostate Specific Ets factor is a recently identified transcriptional activator that is overexpressed in prostate cancer. To determine whether this gene is overexpressed in breast cancer, we performed a virtual Northern blot using data available online at the Cancer Genome Anatomy Project website. Ninety-five SAGE libraries were probed with a unique sequence tag to the Prostate Specific Ets gene. The results indicate that Prostate Specific Ets is expressed in 14 out of 15 breast cancer libraries (93%), nine out of 10 prostate cancer libraries (90%), three out of 40 libraries from other cancers (7.5%), and four out of 30 normal tissue libraries (13%). To determine the possibility that the Prostate Specific Ets gene is a novel marker for detection of metastatic breast cancer in axillary lymph nodes, quantitative real-time RT–PCR analyses were performed. The mean level of Prostate Specific Ets expression in lymph nodes containing metastatic breast cancer (n=22) was 410-fold higher than in normal lymph node (n=51). A receiver operator characteristic curve analysis indicated that Prostate Specific Ets was overexpressed in 18 out of 22 lymph nodes containing metastatic breast cancer (82%). The receiver operator characteristic curve analysis also indicated that the diagnostic accuracy of the Prostate Specific Ets gene for detection of metastatic breast cancer in axillary lymph nodes was 0.949. These results provide evidence that Prostate Specific Ets is a potentially informative novel marker for detection of metastatic breast cancer in axillary lymph nodes, and should be included in any study that involves molecular profiling of breast cancer

Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $\rho$ and a new two-electron parameter $\eta$. We outline a systematic strategy to determine a new density functional $E(\rho,\eta)$ across the spectrum of possible $\rho$ and $\eta$ values.Comment: 8 pages, 2 figures, 5 table

Quantum Monte Carlo simulations of solids

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