Potential envelope theory and the local energy theorem

We consider a one--particle bound quantum mechanical system governed by a Schr\"odinger operator $\mathscr{H} = -\Delta + v\,f(r)$, where $f(r)$ is an attractive central potential, and $v>0$ is a coupling parameter. If $\phi \in \mathcal{D}(\mathscr{H})$ is a `trial function', the local energy theorem tells us that the discrete energies of $\mathscr{H}$ are bounded by the extreme values of $(\mathscr{H}\phi)/\phi,$ as a function of $r$. We suppose that $f(r)$ is a smooth transformation of the form $f = g(h)$, where $g$ is monotone increasing with definite convexity and $h(r)$ is a potential for which the eigenvalues $H_n(u)$ of the operator $\mathcal{H}=-\Delta + u\, h(r)$, for appropriate $u >0$, are known. It is shown that the eigenfunctions of $\mathcal{H}$ provide local-energy trial functions $\phi$ which necessarily lead to finite eigenvalue approximations that are either lower or upper bounds. This is used to extend the local energy theorem to the case of upper bounds for the excited-state energies when the trial function is chosen to be an eigenfunction of such an operator $\mathcal{H}$. Moreover, we prove that the local-energy approximations obtained are identical to `envelope bounds', which can be obtained directly from the spectral data $H_n(u)$ without explicit reference to the trial wave functions

COMPTEL solar flare measurements

We review some of the highlights of the COMPTEL measurements of solar flares. These include images of the Sun in γ rays and neutrons. One of the important features of the COMPTEL instrument is its capability to measure weak fluxes of γ rays and neutrons in the extended phase of flares. These data complement the spectra taken with the COMPTEL burst spectrometer and the telescope during the impulsive phase of flares. We focus our attention on some of these general capabilities of the instrument and the latest results of two long‐duration γ‐ray flares, i.e., 11 and 15 June 199

Spectroelectrochemical Elucidation of the Kinetics of Two Closely Spaced Electron Transfers

The use of spectroelectrochemistry to facilitate the analysis of an EE mechanism was reported in this work. Using a set of spectra as a function of potential, the spectra of all three oxidation states were determined using evolving window factor analysis. From these spectra, the concentration of each species in solution was determined for each potential. Using these data, the current was calculated. Unlike the direct measurement of current, the current due to each redox process was determined, allowing one to analyze each redox process separate from the other. With the use of the Butler–Volmer equation, the redox potential and the heterogeneous electron transfer parameters were measured. The spectrally determined current has the advantage of determining the current due to each redox process which is not generally possible with voltammetric data when the redox potentials are close together. This method was applied to the spectroelectrochemical reduction of Escherichia coli sulfite reductase hemoprotein (SiR-HP) in a phosphate buffer and in the presence of cyanide. The electrochemical parameters (E°’s, k°’s and α’s) for each electron transfer were calculated for both the uncoordinated and cyanide coordinated species. The rates of electron transfer for the siroheme and iron–sulfur cluster were slower than the rates observed for other heme proteins. This is probably due to the fact that this protein is significantly larger than most of the heme protein previously studied. This approach is a powerful tool for two-electron transfers when the E° values are close together

On the Complexity of Random Quantum Computations and the Jones Polynomial

There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical complexity of approximately simulating random quantum computations. We prove that random quantum computations cannot be classically simulated up to a constant total variation distance, under the assumption that (1) the Polynomial Hierarchy does not collapse and (2) the average-case complexity of relative-error approximations of the Jones polynomial matches the worst-case complexity over a constant fraction of random links. Our results provide a straightforward relationship between the approximation of Jones polynomials and the complexity of random quantum computations.Comment: 8 pages, 4 figure

Evaluation of a University-Community Partnership to Provide Home-Based, Mental Health Services for Children from Families Living in Poverty

A university-community partnership is described that resulted in the development of community-based mental health services for young children from families living in poverty. The purpose of this pilot project was to implement an evidence-based treatment program in the homes of an at-risk population of children with significant emotional and behavior problems that were further complicated by developmental delays. Outcomes for 237 children who participated in the clinic’s treatment program over a 2 year period are presented. Comparisons are included between treatment completers and non-completers and the issues of subject attrition, potential subject selection bias, and the generalizability of the results are addressed. The need for more professionals who are trained to address mental health issues in very young children who live in very challenging conditions are discussed

Critical superfluid velocity in a trapped dipolar gas

We investigate the superfluid properties of a dipolar Bose-Einstein condensate (BEC) in a fully three-dimensional trap. Specifically, we calculate a superfluid critical velocity for this system by applying the Landau criterion to its discrete quasiparticle spectrum. We test this critical velocity by direct numerical simulation of condensate depletion as a blue-detuned laser moves through the condensate. In both cases, the presence of the roton in the spectrum serves to lower the critical velocity beyond a critical particle number. Since the shape of the dispersion, and hence the roton minimum, is tunable as a function of particle number, we thereby propose an experiment that can simultaneously measure the Landau critical velocity of a dipolar BEC and demonstrate the presence of the roton in this system.Comment: 5 pages, 4 figures, version accepted to PR