A priori probability that a qubit-qutrit pair is separable

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjecture

Bures distance between two displaced thermal states

The Bures distance between two displaced thermal states and the corresponding geometric quantities (statistical metric, volume element, scalar curvature) are computed. Under nonunitary (dissipative) dynamics, the statistical distance shows the same general features previously reported in the literature by Braunstein and Milburn for two--state systems. The scalar curvature turns out to have new interesting properties when compared to the curvature associated with squeezed thermal states.Comment: 3 pages, RevTeX, no figure

Built environment assessment: Multidisciplinary perspectives.

Context:As obesity has become increasingly widespread, scientists seek better ways to assess and modify built and social environments to positively impact health. The applicable methods and concepts draw on multiple disciplines and require collaboration and cross-learning. This paper describes the results of an expert team׳s analysis of how key disciplinary perspectives contribute to environmental context-based assessment related to obesity, identifies gaps, and suggests opportunities to encourage effective advances in this arena. Evidence acquisition:A team of experts representing diverse disciplines convened in 2013 to discuss the contributions of their respective disciplines to assessing built environments relevant to obesity prevention. The disciplines include urban planning, public health nutrition, exercise science, physical activity research, public health and epidemiology, behavioral and social sciences, and economics. Each expert identified key concepts and measures from their discipline, and applications to built environment assessment and action. A selective review of published literature and internet-based information was conducted in 2013 and 2014. Evidence synthesis:The key points that are highlighted in this article were identified in 2014-2015 through discussion, debate and consensus-building among the team of experts. Results focus on the various disciplines׳ perspectives and tools, recommendations, progress and gaps. Conclusions:There has been significant progress in collaboration across key disciplines that contribute to studies of built environments and obesity, but important gaps remain. Using lessons from interprofessional education and team science, along with appreciation of and attention to other disciplines׳ contributions, can promote more effective cross-disciplinary collaboration in obesity prevention

Molecular orbital calculations of two-electron states for P donor solid-state spin qubits

We theoretically study the Hilbert space structure of two neighbouring P donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position and inter donor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, whilst the magnitude of the double occupancy probability can affect the error rate.Comment: 15 pages (2-column

On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere

Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. For these applications, it is of interest to obtain analytic expressions, and we present the reduction of a number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related series have additional applications in quantum and statistical physics and chemistry.Comment: 17 pages, no figure

Large Dog Relinquishment to Two Municipal Facilities in New York City and Washington, D.C.: Identifying Targets for Intervention

While the overall trend in euthanasia has been decreasing nationally, large dogs are at a higher risk of euthanasia than other sized dogs in most animal shelters in the United States. We hypothesized one way to increase the lives saved with respect to these large dogs is to keep them home when possible. In order to develop solutions to decrease relinquishment, a survey was developed to learn more about the reasons owners relinquish large dogs. The survey was administered to owners relinquishing their dogs at two large municipal facilities, one in New York City and one in Washington, D.C. There were 157 responses between the two facilities. We found both significant similarities and differences between respondents and their dogs from the two cities. We identified opportunities to potentially support future relinquishers and found that targets for interventions are likely different in each community

High-Temperature Expansions of Bures and Fisher Information Priors

For certain infinite and finite-dimensional thermal systems, we obtain --- incorporating quantum-theoretic considerations into Bayesian thermostatistical investigations of Lavenda --- high-temperature expansions of priors over inverse temperature beta induced by volume elements ("quantum Jeffreys' priors) of Bures metrics. Similarly to Lavenda's results based on volume elements (Jeffreys' priors) of (classical) Fisher information metrics, we find that in the limit beta -> 0, the quantum-theoretic priors either conform to Jeffreys' rule for variables over [0,infinity], by being proportional to 1/beta, or to the Bayes-Laplace principle of insufficient reason, by being constant. Whether a system adheres to one rule or to the other appears to depend upon its number of degrees of freedom.Comment: Six pages, LaTeX. The title has been shortened (and then further modified), at the suggestion of a colleague. Other minor change

Homogenization induced by chaotic mixing and diffusion in an oscillatory chemical reaction

A model for an imperfectly mixed batch reactor with the chlorine dioxide-iodine-malonic acid (CDIMA) reaction, with the mixing being modelled by chaotic advection, is considered. The reactor is assumed to be operating in oscillatory mode and the way in which an initial spatial perturbation becomes homogenized is examined. When the kinetics are such that the only stable homogeneous state is oscillatory then the perturbation is always entrained into these oscillations. The rate at which this occurs is relatively insensitive to the chemical effects, measured by the Damkohler number, and is comparable to the rate of homogenization of a passive contaminant. When both steady and oscillatory states are stable, spatially homogeneous states, two possibilities can occur. For the smaller Damkohler numbers, a localized perturbation at the steady state is homogenized within the background oscillations. For larger Damkohler numbers, regions of both oscillatory and steady behavior can co-exist for relatively long times before the system collapses to having the steady state everywhere. An interpretation of this behavior is provided by the one-dimensional Lagrangian filament model, which is analyzed in detail

Ground state of two electrons on concentric spheres

We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79}, 062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several electronic structure models are analyzed, ranging from the mean-field approximation (restricted and unrestricted Hartree-Fock solutions) to configuration interaction expansion, leading to near-exact wave functions and energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the asymptotic expansion for the large-spheres regime are also considered. We also study the position intracules derived from approximate and exact wave functions. We find evidence for the existence of a long-range Coulomb hole in the large-spheres regime, and infer that unrestricted Hartree-Fock theory over-localizes the electrons.Comment: 10 pages, 10 figure

Exchange between deep donors in semiconductors: a quantum defect approach

Exchange interactions among defects in semiconductors are commonly treated within effective-mass theory using a scaled hydrogenic wave-function. However such a wave-function is only applicable to shallow impurities; here we present a simple but robust generalization to treat deep donors, in which we treat the long-range part of the wavefunction using the well established quantum defect theory, and include a model central-cell correction to fix the bound-state eigenvalue at the experimentally observed value. This allows us to compute the effect of binding energy on exchange interactions as a function of donor distance; this is a significant quantity given recent proposals to carry out quantum information processing using deep donors. As expected, exchange interactions are suppressed (or increased), compared to the hydrogenic case, by the greater localization (or delocalization) of the wavefunctions of deep donors (or `super-shallow' donors with binding energy less then the hydrogenic value). The calculated results are compared with a simple scaling of the Heitler-London hydrogenic exchange; the scaled hydrogenic results give the correct order of magnitude but fail to reproduce quantitatively our calculations. We calculate the donor exchange in silicon including inter-valley interference terms for donor pairs along the $\{100\}$ direction, and also show the influence of the donor type on the distribution of nearest-neighbour exchange constants at different concentrations. Our methods can be used to compute the exchange interactions between two donor electrons with arbitrary binding energy.Comment: 11 pages, 10 figures, RevTeX