Adventures of the Coupled Yang-Mills Oscillators: I. Semiclassical Expansion

We study the quantum mechanical motion in the $x^2y^2$ potentials with $n=2,3$, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. These systems show strong stochasticity in the classical limit ($\hbar = 0$) and exhibit a quantum mechanical confinement feature. We calculate the partition function $Z(t)$ going beyond the Thomas-Fermi (TF) approximation by means of the semiclassical expansion using the Wigner-Kirkwood (WK) method. We derive a novel compact form of the differential equation for the WK function. After separating the motion in the channels of the equipotential surface from the motion in the central region, we show that the leading higher-order corrections to the TF term vanish up to eighth order in $\hbar$, if we treat the quantum motion in the hyperbolic channels correctly by adiabatic separation of the degrees of freedom. Finally, we obtain an asymptotic expansion of the partition function in terms of the parameter $g^2\hbar^4t^3$

The potential of phosphorus in clinopyroxene as a geospeedometer: examples from mantle xenoliths

We investigate the potential to use concentrations and zoning patterns of phosphorus (P) in clinopyroxene as indicators of the rates of igneous and metasomatic processes, comparable to recent applications of P in olivine but applicable to more evolved rocks and lower temperatures of crystallization. Few high-P pyroxenes have been previously reported, and none have been analyzed in detail for the mechanism of P enrichment or the implications for mineral growth kinetics. Here, we report the discovery and characteristics of exotic phosphorus-rich secondary clinopyroxene in glassy pockets and veins in composite mantle xenoliths from the Cima Volcanic Field (California, USA) and the Middle Atlas Mountains (Morocco, West Africa). These glass-bearing xenoliths preserve evidence of melt infiltration events and the contrasting behavior of P in their pyroxene crystals constrains the different rates of reaction and extents of equilibration that characterized infiltration in each setting. We report optical petrography and chemical analysis of glasses and minerals for major elements by electron microprobe microanalyzer and trace elements by laser-ablation Inductively Coupled Plasma Mass Spectrometry. The Cima Volcanic Field specimen shows one end-member behavior, with unzoned P-rich clinopyroxene in a melt pocket. We attribute this occurrence to a slow crystallization process that occurred after the melt temperature reached near-equilibrium with the host rock and during which the P concentration in the melt was buffered by apatite saturation. In the Morocco xenolith, by contrast, clinopyroxene exhibits zonation with P increasing all the way to the rim, in contact with the glass. We ascribe this feature to a rapid growth process in which excess P was incorporated into the growing clinopyroxene from a diffusive boundary layer. We demonstrate quantitative agreement between the enrichment of P and other trace elements and their expected diffusion and partitioning behavior during rapid growth. We suggest that P has not been widely reported in clinopyroxene in large part because it has rarely been looked for and that its analysis offers considerable promise as a kinetic indicator both in xenoliths and volcanic rocks

Adventures of the Coupled Yang-Mills Oscillators: II. YM-Higgs Quantum Mechanics

We continue our study of the quantum mechanical motion in the $x^2y^2$ potentials for $n=2,3$, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. In the present paper, we develop a new approach to the calculation of the partition function $Z(t)$ beyond the Thomas-Fermi (TF) approximation by adding a harmonic (Higgs) potential and taking the limit $v\to 0$, where $v$ is the vacuum expectation value of the Higgs field. Using the Wigner-Kirkwood method to calculate higher-order corrections in $\hbar$, we show that the limit $v\to 0$ leads to power-like singularities of the type $v^{-n}$, which reflect the possibility of escape of the particle along the channels in the classical limit. We show how these singularities can be eliminated by taking into account the quantum fluctuations dictated by the form of the potential

Hyperk\"ahler torsion structures invariant by nilpotent Lie groups

We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on $\R^8$ which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex structures are of a special kind, called abelian. We prove that on any 2-step nilpotent Lie group all invariant HKT structures arise from abelian hypercomplex structures. Furthermore, we use a correspondence between abelian hypercomplex structures and subspaces of ${\frak sp}(n)$ to produce continuous families of compact and noncompact of manifolds carrying non isometric HKT structures. Finally, geometrical properties of invariant HKT structures on 2-step nilpotent Lie groups are obtained.Comment: LateX, 12 page

Alterations of Central Liver Metabolism of Pediatric Patients with Non-Alcoholic Fatty Liver Disease

Non-alcoholic fatty liver disease (NAFLD) is the most common chronic liver disease in children and is associated with overweight and insulin resistance (IR). Almost nothing is known about in vivo alterations of liver metabolism in NAFLD, especially in the early stages of non-alcoholic steatohepatitis (NASH). Here, we used a complex mathematical model of liver metabolism to quantify the central hepatic metabolic functions of 71 children with biopsy-proven NAFLD. For each patient, a personalized model variant was generated based on enzyme abundances determined by mass spectroscopy. Our analysis revealed statistically significant alterations in the hepatic carbohydrate, lipid, and ammonia metabolism, which increased with the degree of obesity and severity of NAFLD. Histologic features of NASH and IR displayed opposing associations with changes in carbohydrate and lipid metabolism but synergistically decreased urea synthesis in favor of the increased release of glutamine, a driver of liver fibrosis. Taken together, our study reveals already significant alterations in the NASH liver of pediatric patients, which, however, are differently modulated by the simultaneous presence of IR

PHOSPHORUS ZONING FROM SECONDARY OLIVINE IN MANTLE XENOLITH FROM MIDDLE ATLAS MOUNTAINS (MOROCCO, AFRICA): IMPLICATIONS FOR CRYSTAL GROWTH KINETICS

Συλλέχθηκαν δείγματα μανδυακών ξενολίθων σε επαφή με βασάλτες από το μάαρ Tafraoute του Μαρόκκου. Διαπιστώθηκε η ύπαρξη φλεβών τήγματος που τέμνουν την πρωτογενή στρωμάτωση και σχιστότητα. Για τον πετρογραφικό και χημικό χαρακτηρισμό των φλεβών τήγματος, εφαρμόστηκαν οι τεχνικές της οπτικής μικροσκοπίας και ηλεκτρονικής μικροανάλυσης. Οι φλέβες αποτελούνται από ύελο και κρυστάλλους ολιβίνη, κλινοπυροξένου, πλαγιοκλάστου, σπινελίου και απατίτη. Ο ολιβίνης είναι πλούσιος στην περιφέρειά του σε φώσφορο ~0,3 %κ.β (εκπεφρασμένο ως P2O5). Correlations between Al and P, as well as experimentally determined partition coefficient for P, point towards non-equilibrium partitioning during rapid crystal growth at the end of crystallization. Βασιζόμενοι σε συντελεστές κατανομής φωσφόρου μεταξύ ολιβίνη και τήγματος, και τη σχέση του αργιλίου με το φώσφορο, 1924 καταλήγουμε σε κατανομή σε συνθήκες μη ισορροπίας κατά τη διάρκεια ταχύτατης ανάπτυξης στο τέλος της κρυστάλλωσηςMantle xenolith samples in contact with basalt flows were collected from the Tafraoute maar in Morocco. Discrete melt veins are present in one xenolith sample, crosscutting primary layering and foliation. We used both optical microscopy and electron microprobe analysis to characterize the glasses and minerals in the melt veins. The melt veins consist of glass and crystals of olivine, clinopyroxene, plagioclase, spinel and apatite. The olivine in the melt veins is quite distinct from the same mineral within the matrix due to its characteristic P-enriched rims (up to 0.3 wt.%). Correlations between Al and P, as well as experimentally determined partition coefficient for P, point towards non-equilibrium partitioning during rapid crystal growth at the end of crystallization

Spin Manipulation by Creation of Single-Molecule Radical Cations

All-trans-retinoic acid (ReA), a closed-shell organic molecule comprising only C, H, and O atoms, is investigated on a Au(111) substrate using scanning tunneling microscopy and spectroscopy. In dense arrays single ReA molecules are switched to a number of states, three of which carry a localized spin as evidenced by conductance spectroscopy in high magnetic fields. The spin of a single molecule may be reversibly switched on and off without affecting its neighbors. We suggest that ReA on Au is readily converted to a radical by the abstraction of an electron.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Let