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

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

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

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

Atomic quasi-Bragg diffraction in a magnetic field

We report on a new technique to split an atomic beam coherently with an easily adjustable splitting angle. In our experiment metastable helium atoms in the |{1s2s}^3S_1 M=1> state diffract from a polarization gradient light field formed by counterpropagating \sigma^+ and \sigma^- polarized laser beams in the presence of a homogeneous magnetic field. In the near-adiabatic regime, energy conservation allows the resonant exchange between magnetic energy and kinetic energy. As a consequence, symmetric diffraction of |M=0> or |M=-1> atoms in a single order is achieved, where the order can be chosen freely by tuning the magnetic field. We present experimental results up to 6th order diffraction (24 \hbar k momentum splitting, i.e., 2.21 m/s in transverse velocity) and present a simple theoretical model that stresses the similarity with conventional Bragg scattering. The resulting device constitutes a flexible, adjustable, large-angle, three-way coherent atomic beam splitter with many potential applications in atom optics and atom interferometry.Comment: 4 pages, 5 figure

New Entrepreneurship in Urban Diasporas in our Modern World

ABSTRACT: Entrepreneurship among migrants – often called new, migrant or ethnic entrepreneurship – has over the past years become a significant component of the urban economy in many developed countries. Migrant entrepreneurship has a considerable welfare enhancing impact on the city, notably a contribution to innovation and growth, creation of new jobs for less favoured population groups, advancement of benefits from cultural diversity, and reinforcement of economic opportunities related to international connectivity. The present paper aims to investigate the backgrounds of migrant entrepreneurship in large Dutch cities, in particular, the critical success factors of business performance of these entrepreneurs in relation to their ethnic background, their levels of skill, and other specific and general contextual factors. To address the drivers of break-out strategies for new markets, a sample of second-generation Moroccan entrepreneurs is extensively interviewed to extract detailed information at a micro business level. The wealth of qualitative information on both input factors and output (performance) achievements is next systematically coded in a qualitative survey table which is converted into a format that is suitable for application of a rough set analysis. This is an artificial intelligence technique that is able to extract and identify the set of combinations of different drivers that altogether make up for a final outcome. The results show that longer stay in the host country, male gender, family network support and education of the entrepreneurs concerned are critical variables for the business performance of these urban diaspora entrepreneurs. KEYWORDS: Migrant entrepreneurship, break-out strategies, change agents, second-generation migrant entrepreneurs, urban economy, innovation, cultural diversity, international connectivity, business performance, rough set analysis, urban diaspora entreprene

Numerical simulations on the motion of atoms travelling through a standing-wave light field

The motion of metastable helium atoms travelling through a standing light wave is investigated with a semi-classical numerical model. The results of a calculation including the velocity dependence of the dipole force are compared with those of the commonly used approach, which assumes a conservative dipole force. The comparison is made for two atom guiding regimes that can be used for the production of nanostructure arrays; a low power regime, where the atoms are focused in a standing wave by the dipole force, and a higher power regime, in which the atoms channel along the potential minima of the light field. In the low power regime the differences between the two models are negligible and both models show that, for lithography purposes, pattern widths of 150 nm can be achieved. In the high power channelling regime the conservative force model, predicting 100 nm features, is shown to break down. The model that incorporates velocity dependence, resulting in a structure size of 40 nm, remains valid, as demonstrated by a comparison with quantum Monte-Carlo wavefunction calculations.Comment: 9 pages, 4 figure

Correlation effects in bistability at the nanoscale: steady state and beyond

The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the non-equilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born (2B) and GW level. Assuming the existence of a steady-state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate if and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.Comment: 13 pages, 12 figure