Equation of state and structural characterization of Cu4I4{PPh2(CH2CH = CH2)}4 under pressure

Combined high pressure single crystal X-ray diffraction experiments and ab initio simulations based on the density functional theory have been performed on a copper(I) iodide cluster formulated [Cu₄I₄{PPh₂(CH₂CH?=?CH₂)}₄] under high pressure up to 5?GPa. An exhaustive study of compressibility has been done by means of determination of isothermal equations of state and structural changes with pressure at 298?K taking advantage of the single crystal is more precise than powder X-ray diffraction for this type of experiments. It allows us to report the evidence of the existence of an isostructural phase transition of second order at 2.3?GPa not detected so far.     

Charge and magnetic moment of the neutrino in the background field method and in the linear R_{\xi}^L gauge

We present a computation of the charge and the magnetic moment of the neutrino in the recently developed electro-weak Background Field Method and in the linear gauge. First, we deduce a formal Ward-Takahashi identity which implies the immediate cancellation of the neutrino electric charge. This Ward-Takahashi identity is as simple as that for QED. The computation of the (proper and improper) one loop vertex diagrams contributing to the neutrino electric charge is also presented in an arbitrary gauge, checking in this way the Ward-Takahashi identity previously obtained. Finally, the calculation of the magnetic moment of the neutrino, in the minimal extension of the Standard Model with massive Dirac neutrinos, is presented, showing its gauge parameter and gauge structure independence explicitly. Received: 6 July 1999 / Revised version: 27 October 1999 / Published online: 27 January 2000     

On Co-Circular Central Configurations in the Four and Five Body-Problems for Homogeneous Force Law

We study the central configurations (cc for short) for four masses arranged on a common circle (called co-circular cc) in two different situations, namely with no mass inside and later adding a fifth mass at the center of the circle. In the former, we focus the kite shape configurations by proving the existence of a one-parameter family of cc which goes from the kite containing an equilateral triangle up to the square shape. After, by putting a fifth mass at the center, we feature the planar cc of five bodies as a tensor of corange two see, “Albouy and Chenciner (Invent Math 131:151–184, 1998)” and we prove that cc is stacked see, “Hampton (Nonlinearity 18:2299–2304, 2005b)” in a such way that the center of mass of the four bodies should be the center of the circle. We emphasize that our approach includes not only the Newtonian force law, but the homogeneous ones with exponent $a\le -1$ a ≤ ? 1 .     

Chiral phase transition in two-dimensional supramolecular assemblies of prochiral molecules

The self-assembly of the rodlike two-dimensional chiral molecule 4-[trans-2-(pyrid-4-yl-vinyl)] benzoic acid on the Cu(100) surface has been investigated by scanning tunneling microscopy. Upon adsorption at T>or=300 K, the molecules are deprotonated and assemble in parquet patterns when the coverage remains below a critical value. Corresponding high-resolution data reveal that the ordering implies mesoscopic chiral resolution as a result of chiroselective interactions (i.e., two domains comprise exclusively one enantiomer). When the critical coverage is exceeded, an abrupt transition to a single racemic phase is observed with a different lateral molecular coupling scheme. The shifting of the subtle balance between the weak lateral coupling, substrate bonding, and the packing requirements encountered with the increased molecular coverage is suggested to be the driving force for this homochiral-to-heterochiral phase transition.     

Interaction cost of nonlocal gates

We introduce the interaction cost of a nonlocal gate as the minimal time of interaction required to perform the gate when assisting the process with fast local unitaries. This cost, of interest both in the areas of quantum control and quantum information, depends on the specific interaction, and allows one to compare in an operationally meaningful manner any two nonlocal gates. In the case of a two-qubit system, an analytical expression for the interaction cost of any unitary operation given any coupling Hamiltonian is obtained. One gate may be more time consuming than another for any possible interaction. This defines a partial order structure in the set of nonlocal gates, that compares their degree of nonlocality. We analytically characterize this partial order in a region of the set of two-qubit gates.     

Total synthesis of (15R)- and (15S)-F(2t)-isoprostanes by a biomimetic process using the cyclization of acyclic dihydroxylated octa-5,7-dienyl radicals

We report a new route to F(2t)-IsoP (formerly named 8-epi-PGF(2alpha)) using a biomimetic radical cyclization of a highly functionalized C20 precursor. The strategy employed gives a beta-hydroxy free radical followed by molecular oxygen trapping, which is an unusual method for quenching carbon free radicals. We observed the formation of unique diastereoisomers (15R)- and (15S)-F(2t)-IsoP. This result is consistent with a strong stereoelectronic control associated with a steric effect initiated by the side chains alpha and omega on the cyclopentane ring.