Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions, We illustrate how this general formalism applier; to construct multiparametric versions of the supersymmetric t-J and Li models.

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.

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

Relationships between blood pressure and heart rate in the saltwater crocodile Crocodylus porosus

The cardiac limb of the baroreflex loop was studied in the saltwater crocodile Crocodylus porosus, The classical pharmacological methodology using phenylephrine and sodium nitroprusside was used to trigger blood pressure changes, and the resulting alterations in heart rate were analysed quantitatively using a logistic function. Interindividual differences in resting heart rates and blood pressures were observed, but all seven animals displayed clear baroreflex responses. Atropine and sotalol greatly attenuated the response. A maximal baroreflex gain of 7.2 beats min(-1) kPa(-1) was found at a mean aortic pressure of 6.1 kPa, indicating the active role of the baroreflex in a wide pressure range encompassing hypotensive and hypertensive states. At the lowest mean aortic pressures (5.0 kPa), the synergistic role of the pulmonary-to-systemic shunt in buffering the blood pressure drop also contributes to blood pressure regulation, Pulse pressure showed a better correlation,vith heart rate and also a higher gain than mean aortic, systolic or diastolic pressures, and this is taken as an indicator of the existence of a differential control element working simultaneously with a linear proportional element.

Heart rate, blood lactate and kinematic data of elite colts (under-19) rugby union players during competition

Physiological and kinematic data were collected from elite under-19 rugby union players to provide a greater understanding of the physical demands of rugby union. Heart rate, blood lactate and time-motion analysis data were collected from 24 players (mean +/- s((x) over bar): body mass 88.7 +/- 9.9 kg, height 185 +/- 7 cm, age 18.4 +/- 0.5 years) during six competitive premiership fixtures. Six players were chosen at random from each of four groups: props and locks, back row forwards, inside backs, outside backs. Heart rate records were classified based on percent time spent in four zones (>95%, 85-95%, 75-84%, <75% HRmax). Blood lactate concentration was measured periodically throughout each match, with movements being classified as standing, walking, jogging, cruising, sprinting, utility, rucking/mauling and scrummaging. The heart rate data indicated that props and locks (58.4%) and back row forwards (56.2%) spent significantly more time in high exertion (85-95% HRmax) than inside backs (40.5%) and outside backs (33.9%) (P < 0.001). Inside backs (36.5%) and outside backs (38.5%) spent significantly more time in moderate exertion (75-84% HRmax) than props and locks (22.6%) and back row forwards (19.8%) (P < 0.05). Outside backs (20.1%) spent significantly more time in low exertion (< 75% HRmax) than props and locks (5.8%) and back row forwards (5.6%) (P < 0.05). Mean blood lactate concentration did not differ significantly between groups (range: 4.67 mmol.l(-1) for outside backs to 7.22 mmol.l(-1) for back row forwards; P < 0.05). The motion analysis data indicated that outside backs (5750 m) covered a significantly greater total distance than either props and locks or back row forwards (4400 and 4080 m, respectively; P < 0.05). Inside backs and outside backs covered significantly greater distances walking (1740 and 1780 m, respectively; P < 0.001), in utility movements (417 and 475 m, respectively; P < 0.001) and sprinting (208 and 340 m, respectively; P < 0.001) than either props and locks or back row forwards (walking: 1000 and 991 m; utility movements: 106 and 154 m; sprinting: 72 and 94 m, respectively). Outside backs covered a significantly greater distance sprinting than inside backs (208 and 340 m, respectively; P < 0.001). Forwards maintained a higher level of exertion than backs, due to more constant motion and a large involvement in static high-intensity activities. A mean blood lactate concentration of 4.8-7.2 mmol.l(-1) indicated a need for 'lactate tolerance' training to improve hydrogen ion buffering and facilitate removal following high-intensity efforts. Furthermore, the large distances (4.2-5.6 km) covered during, and intermittent nature of, match-play indicated a need for sound aerobic conditioning in all groups (particularly backs) to minimize fatigue and facilitate recovery between high-intensity efforts.

Quantum oscillations in quasi-one-dimensional metals with spin-density-wave ground states

We consider the magnetoresistance oscillation phenomena in the Bechgaard salts (TMTSF)(2)X, where X = ClO4, PF6, and AsF6 in pulsed magnetic fields to 51 T. Of particular importance is the observation of a new magnetoresistance oscillation for X = ClO4 in its quenched state. In the absence of any Fermi-surface reconstruction due to anion order at low temperatures, all three materials exhibit nonmonotonic temperature dependence of the oscillation amplitude in the spin-density-wave (SDW) state. We discuss a model where, below a characteristic temperature T* within the SDW state, a magnetic breakdown gap opens. [S0163-1829(99)00904-2].

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground-state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave (LSW) theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)(2)X family of superconducting molecular crystals. The ground-state energy, the staggered magnetization, magnon excitation spectra, and spin-wave velocities are computed as functions of the ratio of the antiferromagnetic exchange between the second and first neighbours, J(2)/J(1). We find that near J(2)/J(1) = 0.5, i.e., in the region where the classical spin configuration changes from a Neel-ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. in this region, the quantum correction to the magnetization is large but finite. This is in contrast to the case for the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J(2)/J(1), the model becomes a set of chains with frustrated interchain coupling. For J(2) > 4J(1), the quantum correction to the magnetization, within LSW theory, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, the quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustrated interchain coupling.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

Increased ovulation rate in Merino ewes immunized against small synthetic peptide fragments of the inhibin alpha subunit

Four experiments were carried out in Merino ewes during a period of 4 years to determine the long-term effects of immunization against different synthetic peptides mimicking the amine terminal of the or subunit of porcine inhibin. Peptides were conjugated to human serum albumin and 100-200 mu g emulsified in Freund's complete adjuvant for the primary immunization. Usually two booster injections were given at monthly intervals with 50-100 mu g conjugated peptide using either incomplete Freund's adjuvant or Montanide : Marcel. In some experiments a further immunization was carried in the next year. Blood samples were taken 10 days after each immunization, during the luteal phase, for estimation of gonadotrophin concentrations and determination of inhibin antibody titres. One day after blood sampling cloprostenol was used to induce luteolysis and laparoscopy was performed in the subsequent oestrous cycle. Immunization of ewes with synthetic peptides 1-32, 1-26, 7-26 and 8-30 resulted in large increases in the ovulation rate (OR). An approximately two-fold increase in OR was observed following the first booster immunization with these peptides and a three- to five-fold increase after the second booster immunization. Immunization with these large peptides resulted in a sustained increase in OR for a period of at least 1 year after the second booster immunization. Of the shorter peptides, peptides 10-26 and 13-26 gave a reasonable ovulatory response, although it was more difficult to obtain a response with peptides 1-16, 8-22, 13-25, 8-19 and 10-19; peptides 7-13 and 1-6 gave no response (but were examined for one breeding season only). The smaller peptides led to lower inhibin antibody titres that were not necessarily associated with increased follicle-stimulating hormone (FSH) or OR. More intensive blood sampling in one experiment showed that following primary immunization against peptide 1-32 there was a transient increase in plasma FSH which did not lead to an increased OR. Moreover, a prolonged period of raised FSH after the first booster was significantly correlated with increased OR. In these animals antibody titres were only slightly increased after primary immunization, but after the first booster immunization higher titres were observed that were significantly correlated with trough FSH values and the subsequent OR. These results are interpreted as showing that (1) to obtain an increase in OR peptides 1-32, 1-26 and 7-26 are suitable as immunogens; (2) smaller peptides are less reliable, often require multiple injections, and the response may be delayed; and (3) an extended period of raised plasma FSH is needed to give a large ovulatory response.

Between-year fluctuations in schizophrenia birth rate and associations with the Southern Oscillation Index, cloud cover and sunshine

Our group have recently proposed that low prenatal vitamin D may be a risk-modifying factor for schizophrenia. Climate variability impacts on vitamin D levels in a population via fluctuations in the amount of available UV radiation. In order to explore this hypothesis, we examined fluctuations in the birthrates for people with schizophrenia born between 1920 and 1967 and three sets of variables strongly associated with UV radiation. These included: (a) the Southern Oscillation Index (SOI), a marker of El Nino which is the most prominent meteorological factor that influences Queensland weather: (b) measures of cloud cover and (c) measures of sunshine. Schizophrenia births were extracted from the Queensland Mental Health register and corrected for background population birth rates. Schizophrenia birth rates had several apparently non-random features in common with the SO1. The prominent SO1 fluctuation event that occurred between 1937 and 1943 is congruent with the most prominent fluctuation in schizophrenia birth rates. The relatively flat profile of SOI activity between 1927 and 1936 also corresponds to the flattest period in the schizophrenia time series. Both time series have prominent oscillations in the 3 ~, year range between 1946 and 1960. Significant associations between schizophrenia birth rates and measures of both sunshine and cloud cover were identified,and all three time series shared periodicity in the 3-4 year range. The analyses suggest that the risk of schizophrenia is higher for those born during times of increased cloud cover,reduced sunshine and positive SO1. These ecological analyses provide initial support for the vitamin D hypothesis, however alternative non-genetic candidate exposures also need to be considered. Other sites with year-to-year fluctuations in cloud cover and sunshine should examine patterns of association between these climate variables and schizophrenia birth rates. The Stanley Foundation supported this project.

Single-spin measurement using single-electron transistors to probe two-electron systems

We present a method for measuring single spins embedded in a solid by probing two-electron systems with a single-electron transistor (SET). Restrictions imposed by the Pauli principle on allowed two-electron states mean that the spin state of such systems has a profound impact on the orbital states (positions) of the electrons, a parameter which SET's are extremely well suited to measure. We focus on a particular system capable of being fabricated with current technology: a Te double donor in Si adjacent to a Si/SiO2, interface and lying directly beneath the SET island electrode, and we outline a measurement strategy capable of resolving single-electron and nuclear spins in this system. We discuss the limitations of the measurement imposed by spin scattering arising from fluctuations emanating from the SET and from lattice phonons. We conclude that measurement of single spins, a necessary requirement for several proposed quantum computer architectures, is feasible in Si using this strategy.

Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

We extend the results of spin ladder models associated with the Lie algebras su(2(n)) to the case of the orthogonal and symplectic algebras o(2(n)), sp(2(n)) where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of XX-type rung interactions and applied magnetic field term.