1,952 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

    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 v→0v\to 0, where vv is the vacuum expectation value of the Higgs field. Using the Wigner-Kirkwood method to calculate higher-order corrections in ℏ\hbar, we show that the limit v→0v\to 0 leads to power-like singularities of the type v−nv^{-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

    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.

    An organic fluorophore-nanodiamond hybrid sensor for photostable imaging and orthogonal, on-demand biosensing

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    Organic fluorescent probes are widely used to detect key biomolecules; however, they often lack the photostability required for extended intracellular imaging. Here we report a new hybrid nanomaterial (peroxynanosensor, PNS), consisting of an organic fluorescent probe bound to a nanodiamond, that overcomes this limitation to allow concurrent and extended cell-based imaging of the nanodiamond and ratiometric detection of hydrogen peroxide. Far-red fluorescence of the nanodiamond offers continuous monitoring without photobleaching, while the green fluorescence of the organic fluorescent probe attached to the nanodiamond surface detects hydrogen peroxide on demand. PNS detects basal production of hydrogen peroxide within M1 polarised macrophages and does not affect macrophage growth during prolonged co-incubation. This nanosensor can be used for extended bio-imaging not previously possible with an organic fluorescent probe, and is spectrally compatible with both Hoechst 33342 and MitoTracker Orange stains for hyperspectral imaging.Malcolm S. Purdey, Patrick K. Capon, Benjamin J. Pullen, Philipp Reineck, Nisha Schwarz, Peter J. Psaltis, Stephen J. Nicholls, Brant C. Gibson and Andrew D. Abel

    Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems

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    We present a quantitative semiclassical treatment of the effects of bifurcations on the spectral rigidity and the spectral form factor of a Hamiltonian quantum system defined by two coupled quartic oscillators, which on the classical level exhibits mixed phase space dynamics. We show that the signature of a pitchfork bifurcation is two-fold: Beside the known effect of an enhanced periodic orbit contribution due to its peculiar ℏ\hbar-dependence at the bifurcation, we demonstrate that the orbit pair born {\em at} the bifurcation gives rise to distinct deviations from universality slightly {\em above} the bifurcation. This requires a semiclassical treatment beyond the so-called diagonal approximation. Our semiclassical predictions for both the coarse-grained density of states and the spectral rigidity, are in excellent agreement with corresponding quantum-mechanical results.Comment: LaTex, 25 pp., 14 Figures (26 *.eps files); final version 3, to be published in Journal of Physics

    Prenatal maternal effects appear to be insensitive to experimental or natural environmental variation:Environmental effects on egg traits

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    In many birds, hatching asynchrony is a common phenomenon, primarily driven by patterns of incubation behaviour. However, experimental results in blue tits (Cyanistes caeruleus) have shown that asynchrony is reduced by intrinsic properties of later eggs that accelerate prenatal development. These intrinsic differences between early and late eggs could be driven by changes in resource availability to females, which are then passively passed onto the egg. Alternatively, it may be due to an anticipatory maternal effect, wherein some signal or resource is actively placed within the egg, which is beneficial to those eggs laid late within the clutch. In order to distinguish between these hypotheses we designed a supplementary feeding experiment, wherein females were provided with food at certain times during the laying phase. This had no discernible effect on development rate, or other egg characteristics, consistent with anticipatory maternal effects. Using a larger dataset we also tested whether natural environmental variation (weather) during egg formation affected maternal investment in eggs. Similarly, egg characteristics were found to be relatively insensitive to the environmental variation, supporting the experimental results.</p

    Incorporating prior knowledge improves detection of differences in bacterial growth rate

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    BACKGROUND: Robust statistical detection of differences in the bacterial growth rate can be challenging, particularly when dealing with small differences or noisy data. The Bayesian approach provides a consistent framework for inferring model parameters and comparing hypotheses. The method captures the full uncertainty of parameter values, whilst making effective use of prior knowledge about a given system to improve estimation. RESULTS: We demonstrated the application of Bayesian analysis to bacterial growth curve comparison. Following extensive testing of the method, the analysis was applied to the large dataset of bacterial responses which are freely available at the web-resource, ComBase. Detection was found to be improved by using prior knowledge from clusters of previously analysed experimental results at similar environmental conditions. A comparison was also made to a more traditional statistical testing method, the F-test, and Bayesian analysis was found to perform more conclusively and to be capable of attributing significance to more subtle differences in growth rate. CONCLUSIONS: We have demonstrated that by making use of existing experimental knowledge, it is possible to significantly improve detection of differences in bacterial growth rate

    Prevalence and predictors of psychological distress before, during, and after a COVID-19 pandemic wave in Switzerland, 2021.

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    There are concerns about acute and long-term mental health effects of the COVID-19 pandemic. This study examined the prevalence and predictors of psychological distress before, during, and after a pandemic wave in Switzerland, 2021. Prevalence of psychological distress was estimated in adults aged 35-96 years using the General Health Questionnaire-12 administered in June 2021 (Specchio-COVID19 cohort, N = 3965), and compared to values from 2003 to 2006 (CoLaus|PsyCoLaus cohort, N = 5667). Anxiety and depression were assessed from February to June 2021 using the Generalised Anxiety Disorder scale-2 and the Patient Health Questionnaire-2, respectively. Prevalence of psychological distress in June 2021, after the pandemic wave (16.0% [95% CI, 14.6%-17.4%]) was comparable to pre-pandemic levels (15.1% [14.0%-16.2%]). Anxiety and depression were highest at the start of the pandemic wave in February 2021, and declined from February to June with the relaxation of measures. Predictors of psychological distress included being younger, female, a single parent, unemployed, a change in working hours or job loss in the past 6 months, greater perceived severity and contagiousness of COVID-19, and self-reported post COVID-19. By June 2021, following a pandemic wave, prevalence of psychological distress in Switzerland was closer to pre-pandemic levels. These findings highlight the need for additional mental health support during times of stricter government policies relating to COVID-19; yet they also suggest that individuals can adapt relatively quickly to the changing context
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