Time-reversal test for stochastic quantum dynamics

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultracold atomic Bose-Einstein condensates to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to 6.022×1023 (Avogadro's number) of particles. This system is realizable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.

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.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Gypsum solubility in seawater, and its application to bauxite residue amelioration

The solubilities and dissolution rates of three gypsum sources (analytical grade (AG), phosphogypsum (PG) and mined gypsum (MG)) with six MG size fractions ((mm) > 2.0, 1.0-2.0, 0.5-1.0, 0.25-0.5, 0.125-0.25, and < 0.125) were investigated in triple deionised water (TDI) and seawater to examine their suitability for bauxite residue amelioration. Gypsum solubility was greater in seawater (3.8 g L 1) than TDI (2.9 g L 1) due to the ionic strength effect, with dissolution in both TDI and seawater following first order kinetics. Dissolution rate constants varied with gypsum source (AR > PG > MG) due to reactivity and surface area differences, with 1:20 gypsum:solution suspensions reaching saturation within 15 s (AR) to 30 min (MG > 2.0). The ability of bauxite residue to adsorb Ca from solution was also examined. The quantity of the total solution Ca adsorbed was found to be small (5 %). These low rates of solution Ca adsorption combined with the comparatively rapid dissolution rates preclude the application of gypsum to the residue sand/seawater slurry as a method for residue amelioration. Instead, direct field application to the residue would ensure more efficient gypsum use. In addition, the formation of a sparingly soluble CaCO3 coating around the gypsum particles after mixing in a highly alkaline seawater/supernatant liquor (SNL) solution greatly reduced the rate of gypsum dissolution.

Mg induced Ca deficiency under alkaline conditions

Little is known about Mg induced Ca deficiency in alkaline conditions, and the relationship between Mg induced Ca deficiency and Na induced Ca deficiency. Dilute nutrient solutions (dominated by Mg) were used to investigate the effect of Ca activity ratio (CAR) on the growth of mungbeans (Vigna radiata (L.) Wilczek cv. Emerald). At pH 9.0, root growth was reduced below a critical CAR of 0.050 (corresponding to 90 % relative root length). Root growth was found to be limited more in Mg solutions than had been previously observed for Na solutions. Using a CAR equation modified with plasma membrane binding constants (to incorporate the differing antagonistic effects of Mg and Na), new critical CAR values were calculated for both Na (0.56) and Mg (0.44) dominated solutions. This modified CAR equation permits the calculation of CAR irrespective of the dominant salt present.

Solution structure of robustoxin, the lethal neurotoxin from the funnel-web spider Atrax robustus

The solution structure of robustoxin, the lethal neurotoxin from the Sydney funnel-web spider Atrax robustus, has been determined from 2D H-1 NMR data, Robustoxin is a polypeptide of 42 residues cross-linked by four disulphide bonds, the connectivities of which were determined from NMR data and trial structure calculations to be 1-15, 8-20, 14-31 and 16-42 (a 1-4/2-6/3-7/5-8 pattern), The structure consists of a small three-stranded, anti-parallel beta-sheet and a series of interlocking gamma-turns at the C-terminus. It also contains a cystine knot, thus placing it in the inhibitor cystine knot motif family of structures, which includes the omega-conotoxins and a number of plant and animal toxins and protease inhibitors. Robustoxin contains three distinct charged patches on its surface, and an extended loop that includes several aromatic and non-polar residues, Both of these structural features may play a role in its binding to the voltage-gated sodium channel. (C) 1997 Federation of European Biochemical Societies.

Short-term spatial diffusion in sigma o+ o- optical molasses

We have measured the spatial diffusion of atoms in a three-dimensional sigma(+)-sigma(-) optical molasses over twenty milliseconds timescale, starting from the initial interaction of the atoms with the molasses. We find that the diffusion constants agree well with a linear model for these short time scales and also compare favourably to other studies of diffusion made over longer time scales. These measurements enable us to quantify the detection method known as freezing molasses. We discuss this method, for detecting and measuring the momentum distribution of cold atoms, which relies on the slow diffusion of atoms in optical molasses to produce a freeze-frame of the spatial distribution of the atoms. This method enables a longer interrogation interval, providing a greatly increased signal-to-noise ratio. (C) 1998 Elsevier Science B.V.

Adsorption characteristics of carbonized bark for phenol and pentachlorophenol

The potential of using carbonized slash pine bark as a substitute for activated carbon was examined in this study. The bark was carbonized by slow heating in nitrogen for 6.5 h to 672 degrees C. The BET-N-2 surface area, average micropore and mesopore diameter, and micropore volume were 332 m(2) g(-1) 21.7 Angstrom, and 0.125 cm(3) g(-1), respectively. The adsorption capacities for phenol and pentachlorophenol (PCP) at pH 2 and pH 8 were evaluated. The Langmuir equation provided a slightly better fit than the Freundlich equation to two sets of phenol data. The calculated Freundlich constants, K = 0.41 - 0.58 mmol/g/(mmol dm(-3))(1/n) and 1/n = 0.30 - 0.41, were lower and higher, respectively, than literature values for activated carbons. The adsorption capacity of the carbonized bark was much lower for PCP than for phenol. The protonated and anionic PCP isotherms were Type II or III, respectively, in the Brunauer classification. The BET equation provided the best fit to protonated PCP isotherm data. The anionic PCP data were fitted to both the BET model and an equation used in the literature to represent phosphate adsorption on activated carbons. Nonlinear regression of the data for both phenol and PCP adsorption with the Freundlich, Langmuir and BET equations generally gave more accurate parameters, compared with the use of linearized equations to obtain the parameters. (C) 1998 SCI.

Improved methods for predicting individual leaf area and leaf senescence in maize (Zea mays)

The ability to predict leaf area and leaf area index is crucial in crop simulation models that predict crop growth and yield. Previous studies have shown existing methods of predicting leaf area to be inadequate when applied to a broad range of cultivars with different numbers of leaves. The objectives of the study were to (i) develop generalised methods of modelling individual and total plant leaf area, and leaf senescence, that do not require constants that are specific to environments and/or genotypes, (ii) re-examine the base, optimum, and maximum temperatures for calculation of thermal time for leaf senescence, and (iii) assess the method of calculation of individual leaf area from leaf length and leaf width in experimental work. Five cultivars of maize differing widely in maturity and adaptation were planted in October 1994 in south-eastern Queensland, and grown under non-limiting conditions of water and plant nutrient supplies. Additional data for maize plants with low total leaf number (12-17) grown at Katumani Research Centre, Kenya, were included to extend the range in the total leaf number per plant. The equation for the modified (slightly skewed) bell curve could be generalised for modelling individual leaf area, as all coefficients in it were related to total leaf number. Use of coefficients for individual genotypes can be avoided, and individual and total plant leaf area can be calculated from total leaf number. A single, logistic equation, relying on maximum plant leaf area and thermal time from emergence, was developed to predict leaf senescence. The base, optimum, and maximum temperatures for calculation of thermal time for leaf senescence were 8, 34, and 40 degrees C, and apply for the whole crop-cycle when used in modelling of leaf senescence. Thus, the modelling of leaf production and senescence is simplified, improved, and generalised. Consequently, the modelling of leaf area index (LAI) and variables that rely on LAI will be improved. For experimental purposes, we found that the calculation of leaf area from leaf length and leaf width remains appropriate, though the relationship differed slightly from previously published equations.

The structure of quantum Lie algebras for the classical series, B-l, C-l and D-l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint --> adjoint We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B-l, C-l and D-l. In the quantum case the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.

Analysis and application of an equilibrium model for in vitro bioassay systems with three components: Receptor, hormone and hormone-binding-protein

A simple theoretical framework is presented for bioassay studies using three component in vitro systems. An equilibrium model is used to derive equations useful for predicting changes in biological response after addition of hormone-binding-protein or as a consequence of increased hormone affinity. Sets of possible solutions for receptor occupancy and binding protein occupancy are found for typical values of receptor and binding protein affinity constants. Unique equilibrium solutions are dictated by the initial condition of total hormone concentration. According to the occupancy theory of drug action, increasing the affinity of a hormone for its receptor will result in a proportional increase in biological potency. However, the three component model predicts that the magnitude of increase in biological potency will be a small fraction of the proportional increase in affinity. With typical initial conditions a two-fold increase in hormone affinity for its receptor is predicted to result in only a 33% increase in biological response. Under the same conditions an Ii-fold increase in hormone affinity for receptor would be needed to produce a two-fold increase in biological potency. Some currently used bioassay systems may be unrecognized three component systems and gross errors in biopotency estimates will result if the effect of binding protein is not calculated. An algorithm derived from the three component model is used to predict changes in biological response after addition of binding protein to in vitro systems. The algorithm is tested by application to a published data set from an experimental study in an in vitro system (Lim et al., 1990, Endocrinology 127, 1287-1291). Predicted changes show good agreement (within 8%) with experimental observations. (C) 1998 Academic Press Limited.

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

Structure determination of the three disulfide bond isomers of alpha-conotoxin GI: A model for the role of disulfide bonds in structural stability

The three possible disulfide bonded isomers of alpha-conotoxin GI have been selectively synthesised and their structures determined by H-1 NMR spectroscopy. alpha-Conotoxin GI derives from the venom of Conus geographus and is a useful neuropharmacological tool as it selectively binds to the nicotinic acetylcholine receptor (nAChR), a ligand-gated ion channel involved in nerve signal transmission. The peptide has the sequence ECCNPACGRHYSC-NH2, and the three disulfide bonded isomers are referred to as GI(2-7;3-13), GI(2-13;3-7) and GI(2-3;7-13). The NMR structure for the native isomer GI(2-7;3-13) is of excellent quality, with a backbone pairwise RMSD of 0.16 Angstrom for a family of 35 structures, and comprises primarily a distorted 3(10),, helix between residues 5 to 11. The two non-native isomers exhibit multiple conformers in solution, with the major populated forms being different in structure both from each other and from the native form. Structure-activity relationships for the native GI(2-7;3-13) as well as the role of the disulfide bonds on folding and stability of the three isomers are examined. It is concluded that the disulfide bonds in alpha-conotoxin GI play a crucial part in determining both the structure and stability of the peptide. A trend for increased conformational heterogeneity was observed in the order of GI(2-7;3-13) < GI(2-13;3-7) < GI(2-3;7-13). It was found that the peptide bond joining Cys2 to Cys3 in GI(2-3;7-13) is predominantly trans, rather than cis as theoretically predicted. These structural data are used to interpret the varying nAChR binding of the non-native forms. A model for the binding of native GI(2-7;3-13) to the mammalian nAChR is proposed, with an alpha-subunit binding face made up of Cys2, Asn4, Pro5, Ala6 and Cys7 and a selectivity face, comprised of Arg9 and His10. These two faces orient the molecule between the alpha and delta subunits of the receptor. The structure of the CCNPAC sequence of the native GI(2-7;3-13) is compared to the structure of the identical sequence from the toxic domain of heat-stable enterotoxins, which forms part of the receptor binding region of the enterotoxins, but which has a different disulfide connectivity. (C) 1998 Academic Press Limited.