Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1999 Elsevier Science B.V.

A method of analysing stream channel response to environmental change: gauge data for the Tully River

Gauging data are available from numerous streams throughout Australia, and these data provide a basis for historical analysis of geomorphic change in stream channels in response to both natural phenomena and human activities. We present a simple method for analysis of these data, and a briefcase study of an application to channel change in the Tully River, in the humid tropics of north Queensland. The analysis suggests that this channel has narrowed and deepened, rather than aggraded: channel aggradation was expected, given the intensification of land use in the catchment, upstream of the gauging station. Limitations of the method relate to the time periods over which stream gauging occurred; the spatial patterns of stream gauging sites; the quality and consistency of data collection; and the availability of concurrent land-use histories on which to base the interpretation of the channel changes.

Determining complicated winding patterns for shim coils using stream functions and the target-field method

In a magnetic resonance imaging equipment, gradient and shim coils are needed to produce a spatially varying magnetic field throughout the sample being imaged. Such coils consist of turns of wire wound on the surface of a cylindrical tube. Shim coils in particular, must sometimes be designed to produce complicated magnetic fields to correct for impurities. Streamline patterns for shim coils are much more complicated than those for gradient coils, In this work we present a detailed analysis of streamline methods and their application to shim coil design, A method is presented for determining the winding patterns to generate these complicated fields. (C) 2002 John Wiley & Sons, Inc.

Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions

Nine classes of integrable open boundary conditions, further extending the one-dimensional U-q (gl (212)) extended Hubbard model, have been constructed previously by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.

Algebraic Bethe ansatz for the anisotropic supersymmetric U model

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=l)(L)C(4)(where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra U-q[gl(2\1)] and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2\1)]. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.

Algebraic Bethe ansatz for integrable extended Hubbard models arising from supersymmetric group solutions

Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.

Clinically significant drug interactions with agents specific for migraine attacks

The drugs which provide specific relief from migraine attacks, the ergopeptides (ergotamine and dihydroergotamine) and the various 'triptans' (notably sumatriptan), are often prescribed for persons already taking various migraine preventative agents, and sometimes drugs for other indications. As a result, migraine-specific drugs may become involved in drug-drug interactions. The migraine-specific drugs all act as agonists at certain subclasses of serotonin (5-hydroxytryptamine; 5-MT) receptor, particularly those of the 5-HT1D subtype, and produce vasoconstriction through these receptor-mediated mechanisms. The oral bioavailabilities of these drugs, particularly those of the ergopeptides, are often incomplete, due to extensive presystemic metabolism. As a result, if migraine-specific agents are coadministered with drugs with vasoconstrictive properties, or with drugs which inhibit the metabolism of the migraine-specific agents, there is a risk of interactions occurring which produce manifestations of excessive vasoconstriction. This can also occur through pharmacodynamic mechanisms, as when ergopeptides or triptans are coadministered with methysergide or propranolol (although a pharmacokinetic element may apply in relation to the latter interaction), or if one migraine-specific agent is used shortly after another. When egopeptide metabolism is inhibited by the presence of macrolide antibacterials, particularly troleandomycin and erythromycin, the resultant interaction can produce ergotism, sometimes leading to gangrene. Similar pharmacokinetic mechanisms, with their vasoconstrictive consequences, probably apply to combination of the ergopeptides with HIV protease inhibitors (indinavir and ritonavir), heparin, cyclosporin or tacrolimus. Inhibition of triptan metabolism by monoamine oxidase A inhibitors, e.g. moclobemide, may raise circulating triptan concentrations, although this does not yet seem to have led to reported clinical problems. Caffeine may cause increased plasma ergotamine concentrations through an as yet inadequately defined pharmacokinetic interaction. However, a direct antimigraine effect of caffeine may contribute to the claimed increased efficacy of ergotamine-caffeine combinations in relieving migraine attacks. Serotonin syndromes have been reported as probable pharmacodynamic consequences of the use of ergots or triptans in persons taking serotonin reuptake inhibitors. There have been two reports of involuntary movement disorders when sumatriptan has been used by patients already taking loxapine. Nearly all the clinically important interactions between the ergopeptide antimigraine agents and currently marketed drugs are likely to have already come to notice. In contrast, new interactions involving the triptans are likely to be recognised as additional members of this family of drugs, with their different patterns of metabolism and pharmacokinetics, are marketed.

Stream-bank shade and larval distribution of the Philippine malaria vector Anopheles flavirostris

The principal malaria vector in the Philippines, Anopheles flavirostris (Ludlow) (Diptera: Culicidae), is regarded as 'shade-loving' for its breeding sites, i.e. larval habitats. This long-standing belief, based on circumstantial observations rather than ecological analysis, has guided larval control methods such as 'stream-clearing' or the removal of riparian vegetation, to reduce the local abundance of An. flavirostris . We measured the distribution and abundance of An. flavirostris larvae in relation to canopy vegetation cover along a stream in Quezon Province, the Philippines. Estimates of canopy openness and light measurements were obtained by an approximation method that used simplified assumptions about the sun, and by hemispherical photographs analysed using the program hemiphot(C) . The location of larvae, shade and other landscape features was incorporated into a geographical information system (GIS) analysis. Early larval instars of An. flavirostris were found to be clustered and more often present in shadier sites, whereas abundance was higher in sunnier sites. For later instars, distribution was more evenly dispersed and only weakly related to shade. The best predictor of late-instar larvae was the density of early instars. Distribution and abundance of larvae were related over time (24 days). This pattern indicates favoured areas for oviposition and adult emergence, and may be predictable. Canopy measurements by the approximation method correlated better with larval abundance than hemispherical photography, being economical and practical for field use. Whereas shade or shade-related factors apparently have effects on larval distribution of An. flavirostris , they do not explain it completely. Until more is known about the bionomics of this vector and the efficacy and environmental effects of stream-clearing, we recommend caution in the use of this larval control method.