Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions and near degeneracy static correlations. In this work we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function $f(r_{12})$ depending on the interelectronic distance $r_{12}$. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function Ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function $f(r_{12})$ needs to diverge for large $r_{12}$ at large internuclear distances while for shorter bond distances it increases as a function of $r_{12}$ to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.Comment: 16 pages, 13 figure

Invariance of the Kohn (sloshing) mode in a conserving theory

It is proven that the center of mass (COM or Kohn) oscillation of a many-body system in a harmonic trap coincides with the motion of a single particle as long as conserving approximations are applied to treat the interactions. The two conditions formulated by Kadanoff and Baym \cite{kb-book} are shown to be sufficient to preserve the COM mode. The result equally applies to zero and finite temperature, as well as to nonequilibrium situations, and to the linear and nonlinear response regimes

Reply to Farine and Aplin: Chimpanzees choose their association and interaction partners

Farine and Aplin (1) question the validity of our study reporting group-specific social dynamics in chimpanzees (2). As alternative to our approach, Farine and Aplin advance a “prenetwork permutation” methodology that tests against random assortment (3). We appreciate Farine and Aplin’s interest and applied their suggested approaches to our data. The new analyses revealed highly similar results to those of our initial approach. We further dispel Farine and Aplin’s critique by outlining its incompatibility to our study system, methodology, and analysis.First, when we apply the suggested prenetwork permutation to our proximity dataset, we again find significant population-level differences in association rates, while controlling for population size [as derived from Farine and Aplin’s script (4); original result, P < 0.0001; results including prenetwork permutation, P < 0.0001]. Furthermore, when we … ↵1To whom correspondence may be addressed. Email: ejcvanleeuwen{at}gmail.com

Automatic alignment for three-dimensional tomographic reconstruction

In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to reconstruct the object. Given noisy and incomplete measurements, the inverse problem is typically solved through a regularized least-squares approach. A challenge for both approaches is that in practice the exact directions and offsets of the x-rays are only known approximately due to, e.g. calibration errors. Such errors lead to artifacts in the reconstructed image. In the case of sufficient sampling and geometrically simple misalignment, the measurements can be corrected by exploiting so-called consistency conditions. In other cases, such conditions may not apply and we have to solve an additional inverse problem to retrieve the angles and shifts. In this paper we propose a general algorithmic framework for retrieving these parameters in conjunction with an algebraic reconstruction technique. The proposed approach is illustrated by numerical examples for both simulated data and an electron tomography dataset

Somatisation and functional impairment in adolescents: longitudinal link with mothers' reactions

Adolescents' somatisation (i.e., the psychological tendency to experience and report multiple physical complaints for which no definite medical cause can be found; SOM) and functional impairment (i.e., all bothersome aftermath of somatisation; FI) were studied in relation to mothers' protection, encouraging/monitoring, and minimisation of physical functional complaints. Besides main effects, interaction effects with other child and parenting characteristics were examined. A total of 990 adolescents and their mothers filled out questionnaires when the adolescents were respectively 12-13 (T1) and 13-14 (T2) years old. At T1, there was a significant relation between mothers' higher amounts of minimisation and adolescents' higher levels of SOM. Further, the link between mothers' higher levels of T1 minimisation and adolescents' higher amounts of T1 FI was significant, but not for adolescents with high levels of depressive mood. Longitudinal analyses revealed that mothers' reactions did not significantly predict adolescents' SOM/FI, nor did adolescents' SOM/FI significantly predict mothers' reactions. Practical implications are discussed

Helium 2 3S - 2 1S metrology at 1557 nm

An experiment is proposed to excite the 'forbidden' 1s2s 3S1 - 1s2s 1S0 magnetic dipole (M1) transition at 1557 nm in a collimated and slow atomic beam of metastable helium atoms. It is demonstrated that an excitation rate of 5000 /s can be realised with the beam of a 2W narrowband telecom fiber laser intersecting the atomic beam perpendicularly. A Doppler-limited sub-MHz spectroscopic linewidth is anticipated. Doppler-free excitation of 2% of trapped and cooled atoms may be realised in a one-dimensional optical lattice geometry, using the 2W laser both for trapping and spectroscopy. The very small (8 Hz) natural linewidth of this transition presents an opportunity for accurate tests of atomic structure calculations of the helium atom. A measurement of the 3He - 4He isotope shift allows for accurate determination of the difference in nuclear charge radius of both isotopes.Comment: accepted for publication in Europhysics Letter

The association between parenting behavior and somatization in adolescents explained by physiological responses in adolescents

Introduction: This study adds to the knowledge on somatization in adolescents by exploring its relation with parenting behavior and the mediating/moderating role of physiological responses in adolescents to parenting behavior. Method: Eighteen adolescents with high and 18 adolescents with low somatization scores and their mothers completed a discussion task, from which observed parenting behavior scores were derived. Skin conductance in adolescents was measured before and during the discussion. Results: For adolescents with high levels of physiological responses, unadaptive parenting was related to a higher chance of high somatization scores. For low physiologically responsive adolescents, the relation between parenting behavior and somatization was not significant. Conclusion: Parenting behavior is not univocally related to somatization in adolescents, but the association depends on physiological responses in adolescents. (C) 2014 Elsevier B.V. All rights reserved

Initialization by measurement of a two-qubit superconducting circuit

We demonstrate initialization by joint measurement of two transmon qubits in 3D circuit quantum electrodynamics. Homodyne detection of cavity transmission is enhanced by Josephson parametric amplification to discriminate the two-qubit ground state from single-qubit excitations non-destructively and with 98.1% fidelity. Measurement and postselection of a steady-state mixture with 4.7% residual excitation per qubit achieve 98.8% fidelity to the ground state, thus outperforming passive initialization.Comment: 5 pages, 4 figures, and Supplementary Information (7 figures, 1 table