Random and free observables saturate the Tsirelson bound for CHSH inequality

Maximal violation of the CHSH-Bell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit near-maximal violations of the CHSH-Bell inequality. To do this, we use the tools of free probability theory to analyze the commutators of large random matrices. Along the way, we introduce the notion of "free observables" which can be thought of as infinite-dimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the fine-grained uncertainty of a sequence of free or random observables, and use this to construct a steering inequality with a large violation

Descriptions of reversed yielding in bending

Existence of Bauschinger effect in bending-unbending of copper beams has been shown from experiment. In modelling of the Bauschinger effect, it is shown that a significant second plastic penetration can occur with the release of the moment required for an elasticplastic bending of a beam. The theory is given for both linear and parabolic hardening material models. The elastic and plastic strains are developed from each hardening model to express the beam curvature of the unstressed neutral axis. Conditions are expressed, using the normalized stress—strain response of a rectangular beam section, for which the release is purely elastic and elastic—plastic. Under the latter the depth to which a second zone of plasticity penetrates is given. Two stress distributions: one for applying the moment and the other for its release, are sufficient to derive the residual stress. Residuals found for parabolic hardening are believed to be more realistic than those from simpler linear or perfectly plastic models, particularly, where a second penetration is evident

Optical Characterization of Indium Arsenide Antimonide Semiconductors Grown by Molecular Beam Epitaxy

The material parameters and crystalline quality of undoped, MBE-grown InAs1-xSbx nearly lattice-matched to (100) GaSb (-0.617% ≤ Δ a-a ≤ +0.708%) similar to material used for mid-infrared semiconductor lasers were determined by optical characterization. Absorption measurements at temperatures between 6-295 K determined the energy gap and wavelength-dependent absorption coefficient for each sample. The compositional dependence of the energy gap was anomalous when compared to previously reported data, suggesting phase separation existed in the material. The samples were also studied by temperature- and excitation-dependent photoluminescence (PL), which, for the majority of cases, showed only a single band-edge peak, identified by comparison with the absorption data. PL linewidths as narrow as 4.3 meV and LO-phonon replicas indicated high material quality, but the shift of the PL peak to higher energies with increased excitation was greater than expected from band filling alone, and underscored the likelihood of phase separation. Extrinsic PL peaks were also observed from one undoped sample, and identified a F-B transition at 4-7 meV and a DAP transition at 10-14 meV below the band edge. Characterization of InAs1-xSbx:Be identified the Be acceptor energy as \u3e30 meV above the valence band

Creative Assignments in Upper Level Undergraduate Courses Inspired by Mentoring Undergraduate Research Projects

This article describes methods and approaches for incorporating creative projects in undergraduate mathematics courses for students of engineering and computer science in an urban community college. The topics and the grading rubrics of the projects go way beyond standard homework questions and contain elements of finding own project, incorporating historical background, inventing own questions and exercises, or demonstrating experiments to illustrate some aspects of the project. After analyzing challenges and outcomes of these projects, I identified several skills which help students be successful, including the skills of creativity. These skills are writing, oral presentation, math skills, and collaboration skills. I present ways to support students in evaluating these skills precisely and improving them over the time of the course. Then I present several examples of student projects, including students\u27 solutions, and insight into how the students demonstrated creative approaches to solving the problems. The paper concludes with suggestions for implementing the projects and an assessment of the projects from the students and instructor perspectives