von Neumann spin measurements with Rashba fields

We show that dynamics in the spin-orbit coupling field simulate the von Neumann measurement of a particle spin. We demonstrate how the measurement influences the spin and coordinate evolution of a particle by comparing two examples of such a procedure. The first example is a simultaneous measurement of spin components, sigma(x) and sigma(y), corresponding to non-commuting operators, which cannot be accurately obtained together at a given time instant due to the Heisenberg uncertainty ratio. By mapping spin dynamics onto a spatial walk, such a procedure determines measurement-time averages of sigma(x) and sigma(y), which can already be precisely evaluated in a single short-time measurement. The other, qualitatively different, example is the spin of a one-dimensional particle in a magnetic field. Here, the measurement outcome depends on the angle between the spin-orbit coupling and magnetic fields. These results can be applied to studies of spin-orbit coupled cold atoms and electrons in solids.

Triel Bonds, pi-Hole-pi-Electrons Interactions in Complexes of Boron and Aluminium Trihalides and Trihydrides with Acetylene and Ethylene

MP2/aug-cc-pVTZ calculations were performed on complexes of aluminium and boron trihydrides and trihalides with acetylene and ethylene. These complexes are linked through triel bonds where the triel center (B or Al) is characterized by the Lewis acid properties through its -hole region while -electrons of C2H2 or C2H4 molecule play the role of the Lewis base. Some of these interactions possess characteristics of covalent bonds, i.e., the Al--electrons links as well as the interaction in the BH3-C2H2 complex. The triel--electrons interactions are classified sometimes as the 3c-2e bonds. In the case of boron trihydrides, these interactions are often the preliminary stages of the hydroboration reaction. The Quantum Theory of Atoms in Molecules as well as the Natural Bond Orbitals approach are applied here to characterize the -hole--electrons interactions.

Anisotropic expansion and SNIa: An open issue

We review the appropriateness of using SNIa observations to detect potential signatures of anisotropic expansion in the Universe. We focus on Union2 and SNLS3 SNIa datasets and use the hemispherical comparison method to detect possible anisotropic features. Unlike some previous works where nondiagonal elements of the covariance matrix were neglected, we use the full covariance matrix of the SNIa data, thus obtaining more realistic and not underestimated errors. As a matter of fact, the significance of previously claimed detections of a preferred direction in the Union2 dataset completely disappears once we include the effects of using the full covariance matrix. Moreover, we also find that such apreferred direction is aligned with the orthogonal direction of the SDSS observational plane and this suggests a clear indication that the SDSS subsample of the Union2 dataset introduces a significant bias, making the detected preferred direction unphysical. We thus find that current SNIa surveys are inappropriate to test anisotropic features due to their highly non-homogeneous angular distribution in the sky. In addition, after removal of the highest in homogeneous sub-samples, the number of SNIa is too low. Finally, we take advantage of the particular distribution of SNLS SNIa sub- sample in the SNLS3 data set, in which the observations were taken along four different directions. We fit each direction independently and find consistent results at the 1 sigma level. Although the likelihoods peak at relatively different values of Omega(m), the low number of data along each direction gives rise to large errors so that the likelihoods are sufficiently broad as to overlap within 1 sigma. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons. org/licenses/by/4.0/).