Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Half-Filled Layered Organic Superconductors and the Resonating-Valence-Bond Theory of the Hubbard-Heisenberg Model

We present a resonating-valence-bond theory of superconductivity for the Hubbard-Heisenberg model on an anisotropic triangular lattice. Our calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta('), kappa, and lambda phases of (BEDT-TTF)(2)X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)(2)X [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a d(x)(2)-y(2) superconductor with a small superfluid stiffness and a pseudogap with d(x)(2)-y(2) symmetry.

On the relationship between the critical temperature and the London penetration depth in layered organic superconductors

We present an analysis of previously published measurements of the London penetration depth of layered organic superconductors. The predictions of the BCS theory of superconductivity are shown to disagree with the measured zero temperature, in plane, London penetration depth by up to two orders of magnitude. We find that fluctuations in the phase of the superconducting order parameter do not determine the superconducting critical temperature as the critical temperature predicted for a Kosterlitz–Thouless transition is more than an order of magnitude greater than is found experimentally for some materials. This places constraints on theories of superconductivity in these materials.

Random numbers from astronomical imaging

This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined.

Achromatic optical phase shifter/modulator

We propose and demonstrate, theoretically and experimentally, a novel achromatic optical phase shifter modulator based on a frequency-domain optical delay line configured to maintain zero group delay as variable phase delay is generated by means of tilting a mirror. Compared with previously reported phase shifter modulators, e.g., based on the Pancharatnam (geometric) phase, our device is high speed and polarization insensitive and produces a large, bounded phase delay that, uniquely, is one-to-one mapped to a measurable parameter, the tilt angle.

Development of a physical and genetic map of the virulent Wolbachia strain wMelPop

We report here the construction of a physical and genetic map of the virulent Wolbachia strain, wMelPop. This map was determined by ordering 28 chromosome fragments that resulted from digestion with the restriction endonucleases FseI, ApaI, SmaI, and AscI and were resolved by pulsed-field gel electrophoresis. Southern hybridization was done with 53 Wolbachia-specific genes as probes in order to determine the relative positions of these restriction fragments and use them to serve as markers. Comparison of the resulting map with the whole genome sequence of the closely related benign Wolbachia strain, wMel, shows that the two genomes are largely conserved in gene organization with the exception of a single inversion in the chromosome.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

A two-phase strategy for detecting recombination in nucleotide sequences

Genetic recombination can produce heterogeneous phylogenetic histories within a set of homologous genes. Delineating recombination events is important in the study of molecular evolution, as inference of such events provides a clearer picture of the phylogenetic relationships among different gene sequences or genomes. Nevertheless, detecting recombination events can be a daunting task, as the performance of different recombination-detecting approaches can vary, depending on evolutionary events that take place after recombination. We previously evaluated the effects of post-recombination events on the prediction accuracy of recombination-detecting approaches using simulated nucleotide sequence data. The main conclusion, supported by other studies, is that one should not depend on a single method when searching for recombination events. In this paper, we introduce a two-phase strategy, applying three statistical measures to detect the occurrence of recombination events, and a Bayesian phylogenetic approach to delineate breakpoints of such events in nucleotide sequences. We evaluate the performance of these approaches using simulated data, and demonstrate the applicability of this strategy to empirical data. The two-phase strategy proves to be time-efficient when applied to large datasets, and yields high-confidence results.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.

Hysteresis and phase transitions in a single partially internally wetted catalyst pellet: Thermogravimetric studies

The hydrogenation of cyclohexene over palladium supported in a microporous gamma-alumina pellet is studied thermogravimetrically with a view to measuring the extent of partial internal wetting associated with the different steady state branches. As many as three steady state branches having significantly different degrees of internal wetting and reaction rates, with transitions between them, are confirmed from observations of catalyst weight change. It is seen that with reduction in catalyst activity the middle branch, obtained by condensation from a vapor filled pellet, is much more prominent without showing an evaporative transition for the range of hydrogen partial pressures used here. The catalyst activity is therefore an important parameter affecting the structure of the steady state branches. Hysteresis effects are found to occur, and the thermogravimetric results also confirm the importance of history in determining the catalyst state. The measured degree of wetting is in accordance with that estimated from a mathematical model incorporating capillary condensation effects in addition to reaction-diffusion phenomena. The same model also satisfactorily interprets the reaction rate variations and transitions seen in the present work.

p-cresol as a reversible acylium ion scavenger in solid-phase peptide synthesis

In this work we have defined the nature of the p-cresol and p-thiocresol adducts generated from acylium ions during HF cleavage, following contemporary Boc/benzyl solid-phase peptide synthesis. Contrary to the results in previous reports, we found that both p-cresol and p-thiocresol predominantly form. aryl esters under typical cleavage conditions. Initially we investigated a number of small peptides containing either a single glutamate residue or a C-terminal long-chain amino acid which allowed us to unambiguously characterize the scavenged side products. Whereas, the p-cresol esters are stable at 0 degrees C they rearrange irreversibly at higher temperatures (5-20 degrees C) to form aryl ketones. By contrast, p-thiocresol esters do not undergo a Fries rearrangement but readily undergo further additions of p-thiocresol to form ketenebisthioacetals and trithio ortho esters, even at low temperatures. Importantly, we found by LC/MS and FT-ICR MS analysis that peptides containing p-cresol esters at glutamyl side chains are susceptible to amidation and fragmentation reactions at these sites during standard mild base workup procedures. The significance of these side reactions was further demonstrated in the synthesis of neutrophil immobilization factor, a 26-residue peptide, containing four glutamic acid residues. The side reactions were largely avoided by mild hydrogen peroxide-catalyzed hydrolysis which converted the p-cresol adducts to the free carboxylic acids in near quantitative yield. The choice of p-cresol as a reversible acylium ion scavenger when coupled with the simple workup conditions described is broadly applicable to Boc/benzyl peptide synthesis and will significantly enhance the quality of peptides produced.

Spin-glass dynamics

Spin glasses are magnetic systems with conflicting and random interactions between the individual spins. The dynamics of spin glasses, as of structural glasses, reflect their complexity. Both in experimental and numerical work the relaxation below the freezing temperature depends strongly on the annealing conditions (aging) and, above the freezing point, relaxation in equilibrium is slow and non-exponential, In this Forum, observed characteristics of the dynamics were summarized and the physical models proposed to explain them were outlined. (C) 1998 Elsevier Science B.V. All rights reserved.

Improved one-step solid-phase extraction method for morphine, morphine-3-glucuronide, and morphine-6-glucuronide from plasma and quantitation using high-performance liquid chromatography with electrochemical detection

This communication describes an improved one-step solid-phase extraction method for the recovery of morphine (M), morphine-3-glucuronide (M3G), and morphine-6-glucuronide (M6G) from human plasma with reduced coextraction of endogenous plasma constituents, compared to that of the authors' previously reported method. The magnitude of the peak caused by endogenous plasma components in the chromatogram that eluted immediately before the retention time of M3G has been reduced (similar to 80%) significantly (p < 0.01) while achieving high extraction efficiencies for the compounds of interest, viz morphine, M6G, and M3G (93.8 +/- 2.5, 91.7 +/- 1.7, and 93.1 +/- 2.2%, respectively). Furthermore, when the improved solid-phase extraction method was used, the extraction cartridge-derived late-eluting peak (retention time 90 to 100 minutes) reported in our previous method, was no longer present in the plasma extracts. Therefore the combined effect of reducing the recovery of the endogenous components of plasma that chromatographed just before the retention time of M3G and the removal of the late-eluting, extraction cartridge-derived peak has resulted in a decrease in the chromatographic run-time to 20 minutes, thereby increasing the sample throughput by up to 100%.