1,725 research outputs found

    Variational collocation for systems of coupled anharmonic oscillators

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    We have applied a collocation approach to obtain the numerical solution to the stationary Schr\"odinger equation for systems of coupled oscillators. The dependence of the discretized Hamiltonian on scale and angle parameters is exploited to obtain optimal convergence to the exact results. A careful comparison with results taken from the literature is performed, showing the advantages of the present approach.Comment: 14 pages, 10 table

    Changes in the expression of the type 2 diabetes-associated gene VPS13C in the β cell are associated with glucose intolerance in humans and mice

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    Single nucleotide polymorphisms (SNPs) close to the VPS13C, C2CD4A and C2CD4B genes on chromosome 15q are associated with impaired fasting glucose and increased risk of type 2 diabetes. eQTL analysis revealed an association between possession of risk (C) alleles at a previously implicated causal SNP, rs7163757, and lowered VPS13C and C2CD4A levels in islets from female (n = 40, P < 0.041) but not from male subjects. Explored using promoter-reporter assays in β-cells and other cell lines, the risk variant at rs7163757 lowered enhancer activity. Mice deleted for Vps13c selectively in the β-cell were generated by crossing animals bearing a floxed allele at exon 1 to mice expressing Cre recombinase under Ins1 promoter control (Ins1Cre). Whereas Vps13cfl/fl:Ins1Cre (βVps13cKO) mice displayed normal weight gain compared with control littermates, deletion of Vps13c had little effect on glucose tolerance. Pancreatic histology revealed no significant change in β-cell mass in KO mice vs. controls, and glucose-stimulated insulin secretion from isolated islets was not altered in vitro between control and βVps13cKO mice. However, a tendency was observed in female null mice for lower insulin levels and β-cell function (HOMA-B) in vivo. Furthermore, glucose-stimulated increases in intracellular free Ca2+ were significantly increased in islets from female KO mice, suggesting impaired Ca2+ sensitivity of the secretory machinery. The present data thus provide evidence for a limited role for changes in VPS13C expression in conferring altered disease risk at this locus, particularly in females, and suggest that C2CD4A may also be involved

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

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    We continue our study of the quantum mechanical motion in the x2y2x^2y^2 potentials for n=2,3n=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)Z(t) beyond the Thomas-Fermi (TF) approximation by adding a harmonic (Higgs) potential and taking the limit v0v\to 0, where vv 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 v0v\to 0 leads to power-like singularities of the type vnv^{-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

    Accuracy of the Semi--Classical Approximation: the Pullen Edmonds Hamiltonian

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    A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the resonant harmonic oscillator. A perturbative interpretation is obtained of the recently observed phenomenon of the accuracy decrease on the approximation of individual energy levels at the increase of the principal quantum number. Moreover, the accuracy provided by the semiclassical approximation formula is on the average the same as that provided by quantum perturbation theory.Comment: 12 pages, 5 figures (available upon request to the authors), LaTex, DFPD/93/TH/47, to be published in Nuovo Cimento

    Experimental ionization of atomic hydrogen with few-cycle pulses

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    We present the first experimental data on strong-field ionization of atomic hydrogen by few-cycle laser pulses. We obtain quantitative agreement at the 10% level between the data and an {\it ab initio} simulation over a wide range of laser intensities and electron energies

    The Partition Function and Level Density for Yang-Mills-Higgs Quantum Mechanics

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    We calculate the partition function Z(t)Z(t) and the asymptotic integrated level density N(E)N(E) for Yang-Mills-Higgs Quantum Mechanics for two and three dimensions (n=2,3n = 2, 3). Due to the infinite volume of the phase space Γ\Gamma on energy shell for n=2n= 2, it is not possible to disentangle completely the coupled oscillators (x2y2x^2 y^2-model) from the Higgs sector. The situation is different for n=3n = 3 for which Γ\Gamma is finite. The transition from order to chaos in these systems is expressed by the corresponding transitions in Z(t)Z(t) and N(E)N(E), analogous to the transitions in adjacent level spacing distribution from Poisson distribution to Wigner-Dyson distribution. We also discuss a related system with quartic coupled oscillators and two dimensional quartic free oscillators for which, contrary to YMHQM, both coupling constants are dimensionless.Comment: 10 pages, LaTeX; minor changes; version accepted for publication as a Letter in J. Phys.
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