Maximal violation of Bell inequalities by position measurements

We show that it is possible to find maximal violations of the CHSH-Bell inequality using only position measurements on a pair of entangled non-relativistic free particles. The device settings required in the CHSH inequality are done by choosing one of two times at which position is measured. For different assignments of the "+" outcome to positions, namely to an interval, to a half line, or to a periodic set, we determine violations of the inequalities, and states where they are attained. These results have consequences for the hidden variable theories of Bohm and Nelson, in which the two-time correlations between distant particle trajectories have a joint distribution, and hence cannot violate any Bell inequality.Comment: 13 pages, 4 figure

Gauss Sums and Quantum Mechanics

By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved. The toroidal nature of the classical phase space leads to discrete position and momentum, and hence discrete time. The corresponding `path integrals' are finite sums whose normalisations are derived and which are shown to intertwine cyclicity and discreteness to give a finite version of Kelvin's method of images.Comment: 14 pages, LaTe

A seesaw-lever force-balancing suspension design for space and terrestrial gravity-gradient sensing

We present the design, fabrication, and characterization of a seesaw-lever force-balancing suspension for a silicon gravity-gradient sensor, a gravity gradiometer, that is capable of operation over a range of gravity from 0 to 1 g. This allows for both air and space deployment after ground validation. An overall rationale for designing a microelectromechanical systems(MEMS) gravity gradiometer is developed, indicating that a gravity gradiometer based on a torsion-balance, rather than a differential-accelerometer, provides the best approach. The fundamental micromachined element, a seesaw-lever force-balancing suspension, is designed with a low fundamental frequency for in-plane rotation to response gravity gradient but with good rejection of all cross-axis modes. During operation under 1 g, a gravitational force is axially loaded on two straight-beams that perform as a stiff fulcrum for the mass-connection lever without affecting sensitive in-plane rotational sensing. The dynamics of this suspension are analysed by both closed-form and finite element analysis, with good agreement between the two. The suspension has been fabricated using through-wafer deep reactive-ion etching and the dynamics verified both in air and vacuum. The sensitivity of a gravity gradiometer built around this suspension will be dominated by thermal noise, contributing in this case a noise floor of around 10 E/Hz−−−√10 E/Hz (1 E = 10−9/s2) in vacuum. Compared with previous conventional gravity gradiometers, this suspension allows a gradiometer of performance within an order of magnitude but greatly reduced volume and weight. Compared with previous MEMS gravity gradiometers, our design has the advantage of functionality under Earth gravity

De Branges spaces and Krein's theory of entire operators

This work presents a contemporary treatment of Krein's entire operators with deficiency indices $(1,1)$ and de Branges' Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown mathematicians. Remarkably, entire operators and de Branges spaces are intimately connected and the interplay between them has had an impact in both spectral theory and the theory of functions. This work exhibits the interrelation between Krein's and de Branges' theories by means of a functional model and discusses recent developments, giving illustrations of the main objects and applications to the spectral theory of difference and differential operators.Comment: 37 pages, no figures. The abstract was extended. Typographical errors were corrected. The bibliography style was change

A local-global principle for linear dependence of noncommutative polynomials

A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the proof yields generalizations to directional local linear dependence and evaluations in general algebras over fields of arbitrary characteristic. A main feature of the proof is that it makes it possible to deduce bounds on the size of the matrices where the (directional) local linear dependence needs to be tested in order to establish linear dependence.Comment: 8 page

Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems

The phenomenon of super-radiance (Dicke effect, coherent spontaneous radiation by a gas of atoms coupled through the common radiation field) is well known in quantum optics. The review discusses similar physics that emerges in open and marginally stable quantum many-body systems. In the presence of open decay channels, the intrinsic states are coupled through the continuum. At sufficiently strong continuum coupling, the spectrum of resonances undergoes the restructuring with segregation of very broad super-radiant states and trapping of remaining long-lived compound states. The appropriate formalism describing this phenomenon is based on the Feshbach projection method and effective non-Hermitian Hamiltonian. A broader generalization is related to the idea of doorway states connecting quantum states of different structure. The method is explained in detail and the examples of applications are given to nuclear, atomic and particle physics. The interrelation of the collective dynamics through continuum and possible intrinsic many-body chaos is studied, including universal mesoscopic conductance fluctuations. The theory serves as a natural framework for general description of a quantum signal transmission through an open mesoscopic system.Comment: 85 pages, 10 figure

Nonprofit governance: Improving performance in troubled economic times

Nonprofit management is currently pressured to perform effectively in a weak economy. Yet, nonprofit governance continues to suffer from unclear conceptions of the division of labor between board of directors and executive directors. This online survey of 114 executive directors aims to provide clarification and recommendations for social administration

Inflammatory cytokines and biofilm production sustain Staphylococcus aureus outgrowth and persistence: A pivotal interplay in the pathogenesis of Atopic Dermatitis

Individuals with Atopic dermatitis (AD) are highly susceptible to Staphylococcus aureus colonization. However, the mechanisms driving this process as well as the impact of S. aureus in AD pathogenesis are still incompletely understood. In this study, we analysed the role of biofilm in sustaining S. aureus chronic persistence and its impact on AD severity. Further we explored whether key inflammatory cytokines overexpressed in AD might provide a selective advantage to S. aureus. Results show that the strength of biofilm production by S. aureus correlated with the severity of the skin lesion, being significantly higher (P < 0.01) in patients with a more severe form of the disease as compared to those individuals with mild AD. Additionally, interleukin (IL)-β and interferon γ (IFN-γ), but not interleukin (IL)-6, induced a concentration-dependent increase of S. aureus growth. This effect was not observed with coagulase-negative staphylococci isolated from the skin of AD patients. These findings indicate that inflammatory cytokines such as IL1-β and IFN-γ, can selectively promote S. aureus outgrowth, thus subverting the composition of the healthy skin microbiome. Moreover, biofilm production by S. aureus plays a relevant role in further supporting chronic colonization and disease severity, while providing an increased tolerance to antimicrobials

A Systematic Review of Argumentation Related to the Engineering-Designed World

Background Across academic disciplines, researchers have found that argumentation‐based pedagogies increase learners\u27 achievement and engagement. Engineering educational researchers and teachers of engineering may benefit from knowledge regarding how argumentation related to engineering has been practiced and studied. Purpose/Hypothesis Drawing from terms and concepts used in national standards for K‐12 education and accreditation requirements for undergraduate engineering education, this study was designed to identify how arguments and argumentation related to the engineering‐designed world were operationalized in relevant literature. Methodology Specified search terms and inclusion criteria were used to identify 117 empirical studies related to engineering argumentation and educational research. A qualitative content analysis was used to identify trends across these studies. Findings Overall, engineering‐related argumentation was associated with a variety of positive learner outcomes. Across many studies, arguments were operationalized in practice as statements regarding whether an existing technology should be adopted in a given context, usually with a limited number of supports (e.g., costs and ethics) provided for each claim. Relatively few studies mentioned empirical practices, such as tests. Most studies did not name the race/ethnicity of participants nor report engineering‐specific outcomes. Conclusions Engineering educators in K‐12 and undergraduate settings can create learning environments in which learners use a range of epistemic practices, including empirical practices, to support a range of claims. Researchers can study engineering‐specific outcomes while specifying relevant demographics of their research participants