Quantum Entanglement in the Two Impurity Kondo Model

In order to quantify quantum entanglement in two impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, $I$. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created (and quantum information processing (QIP) be possible) if the RKKY interaction exchange energy, $I$, is at least several times larger than the Kondo temperature, $T_K$. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.Comment: 7 pages, 3 figures, 1 tabl

Computational design of a pincer phosphinito vanadium ((OPO)V) propane monoxygenation homogeneous catalyst based on the reduction-coupled oxo activation (ROA) mechanism

We propose the vanadium bis(2-phenoxyl)phosphinite pincer complex, denoted (OPO)V, as a low temperature water-soluble catalyst for monoxygenation of propane to isopropanol with functionalization and catalyst regeneration using molecular oxygen. We use DFT study to predict that the barrier for (OPO)V to activate the secondary hydrogen of propane is ΔG‡ = 25.2 kcal/mol at 298K, leading to isopropanol via the new reduction-coupled oxo activation (ROA) mechanism. We then show that reoxidation by dioxygen to complete the cycle is also favorable with ΔG‡ = 6.2 kcal/mol at 298K. We conclude that (OPO)V represents a promising homogeneous catalyst for the monoxygenation of propane and other alkanes (including ethane), warranting experimental validation

Channel kets, entangled states, and the location of quantum information

The well-known duality relating entangled states and noisy quantum channels is expressed in terms of a channel ket, a pure state on a suitable tripartite system, which functions as a pre-probability allowing the calculation of statistical correlations between, for example, the entrance and exit of a channel, once a framework has been chosen so as to allow a consistent set of probabilities. In each framework the standard notions of ordinary (classical) information theory apply, and it makes sense to ask whether information of a particular sort about one system is or is not present in another system. Quantum effects arise when a single pre-probability is used to compute statistical correlations in different incompatible frameworks, and various constraints on the presence and absence of different kinds of information are expressed in a set of all-or-nothing theorems which generalize or give a precise meaning to the concept of ``no-cloning.'' These theorems are used to discuss: the location of information in quantum channels modeled using a mixed-state environment; the $CQ$ (classical-quantum) channels introduced by Holevo; and the location of information in the physical carriers of a quantum code. It is proposed that both channel and entanglement problems be classified in terms of pure states (functioning as pre-probabilities) on systems of $p\geq 2$ parts, with mixed bipartite entanglement and simple noisy channels belonging to the category $p=3$, a five-qubit code to the category $p=6$, etc.; then by the dimensions of the Hilbert spaces of the component parts, along with other criteria yet to be determined.Comment: Latex 32 pages, 4 figures in text using PSTricks. Version 3: Minor typographical errors correcte

Rhodium Bis(quinolinyl)benzene Complexes for Methane Activation and Functionalization

A series of rhodium(III) bis(quinolinyl)benzene (bisq^x) complexes was studied as candidates for the homogeneous partial oxidation of methane. Density functional theory (DFT) (M06 with Poisson continuum solvation) was used to investigate a variety of (bisq^x) ligand candidates involving different functional groups to determine the impact on Rh^(III)(bisq^x)-catalyzed methane functionalization. The free energy activation barriers for methane C H activation and Rh–methyl functionalization at 298 K and 498 K were determined. DFT studies predict that the best candidate for catalytic methane functionalization is Rh^(III) coordinated to unsubstituted bis(quinolinyl)benzene (bisq). Support is also found for the prediction that the η^2-benzene coordination mode of (bisq^x) ligands on Rh encourages methyl group functionalization by serving as an effective leaving group for S_N2 and S_R2 attack

DFT Virtual Screening Identifies Rhodium–Amidinate Complexes As Potential Homogeneous Catalysts for Methane-to-Methanol Oxidation

In the search for new organometallic catalysts for low-temperature selective conversion of CH_4 to CH_3OH, we apply quantum mechanical virtual screening to select the optimum combination of ligand and solvent on rhodium to achieve low barriers for CH_4 activation and functionalization to recommend for experimental validation. Here, we considered Rh because its lower electronegativity compared with Pt and Pd may allow it to avoid poisoning by coordinating media. We report quantum mechanical predictions (including implicit and explicit solvation) of the mechanisms for Rh^(III)(NN) and Rh^(III)(NN^F) complexes [where (NN) = bis(N-phenyl)benzylamidinate and (NN^F) = bis(N-pentafluorophenyl)pentafluorobenzylamidinate] to catalytically activate and functionalize methane using trifluoroacetic acid (TFAH) or water as a solvent. In particular, we designed the (NN^F) ligand as a more electrophilic analogue to the (NN) ligand, and our results predict the lowest transition state barrier (ΔG‡ = 27.6 kcal/mol) for methane activation in TFAH from a pool of four different classes of ligands. To close the catalytic cycle, the functionalization of methylrhodium intermediates was also investigated, involving carbon–oxygen bond formation via S_N2 attack by solvent, or S_R2 attack by a vanadium oxo. Activation barriers for the functionalization of methylrhodium intermediates via nucleophilic attack are lower when the solvent is water, but CH_4 activation barriers are higher. In addition, we have found a correlation between CH_4 activation barriers and rhodium–methyl bond energies that allow us to predict the activation transition state energies for future ligands, as well

Long-Range C–H Bond Activation by Rh^(III)-Carboxylates

Traditional C–H bond activation by a concerted metalation–deprotonation (CMD) mechanism involves precoordination of the C–H bond followed by deprotonation from an internal base. Reported herein is a “through-arene” activation of an uncoordinated benzylic C–H bond that is 6 bonds away from a Rh^(III) ion. The mechanism, which was investigated by experimental and DFT studies, proceeds through a dearomatized xylene intermediate. This intermediate was observed spectroscopically upon addition of a pyridine base to provide a thermodynamic trap

Superconducting p-branes and Extremal Black Holes

In Einstein-Maxwell theory, magnetic flux lines are `expelled' from a black hole as extremality is approached, in the sense that the component of the field strength normal to the horizon goes to zero. Thus, extremal black holes are found to exhibit the sort of `Meissner effect' which is characteristic of superconducting media. We review some of the evidence for this effect, and do present new evidence for it using recently found black hole solutions in string theory and Kaluza-Klein theory. We also present some new solutions, which arise naturally in string theory, which are non-superconducting extremal black holes. We present a nice geometrical interpretation of these effects derived by looking carefully at the higher dimensional configurations from which the lower dimensional black hole solutions are obtained. We show that other extremal solitonic objects in string theory (such as p-branes) can also display superconducting properties. In particular, we argue that the relativistic London equation will hold on the worldvolume of `light' superconducting p-branes (which are embedded in flat space), and that minimally coupled zero modes will propagate in the adS factor of the near-horizon geometries of `heavy', or gravitating, superconducting p-branes.Comment: 22 pages, 2 figure

Cost-effectiveness of alternative methods of surgical repair of inguinal hernia

Objectives: To assess the relative cost-effectiveness of laparoscopic methods of inguinal hernia repair compared with open flat mesh and open non-mesh repair. Methods: Data on the effectiveness of these alternatives came from three systematic reviews comparing: (i) laparoscopic methods with open flat mesh or non-mesh methods; (ii) open flat mesh with open non-mesh repair; and (iii) methods that used synthetic mesh to repair the hernia defect with those that did not. Data on costs were obtained from the authors of economic evaluations previously conducted alongside trials included in the reviews. A Markov model was used to model cost-effectiveness for a five-year period after the initial operation. The outcomes of the model were presented using a balance sheet approach and as cost per hernia recurrence avoided and cost per extra day at usual activities. Results: Open flat mesh was the most cost-effective method of preventing recurrences. Laparoscopic repair provided a shorter period of convalescence and less long-term pain compared with open flat mesh but was more costly. The mean incremental cost per additional day back at usual activities compared with open flat mesh was €38 and €80 for totally extraperitoneal and transabdominal preperitoneal repair, respectively. Conclusions: Laparoscopic repair is not cost-effective compared with open flat mesh repair in terms of cost per recurrence avoided. Decisions about the use of laparoscopic repair depend on whether the benefits (reduced pain and earlier return to usual activities) outweigh the extra costs and intraoperative risks. On the evidence presented here, these extra costs are unlikely to be offset by the short-term benefits of laparoscopic repair.Luke Vale, Adrian Grant, Kirsty McCormack, Neil W. Scott and the EU Hernia Trialists Collaboratio