Addressing student models of energy loss in quantum tunnelling

We report on a multi-year, multi-institution study to investigate student reasoning about energy in the context of quantum tunnelling. We use ungraded surveys, graded examination questions, individual clinical interviews, and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunnelling through a square barrier are particularly common. Students often state that tunnelling particles lose energy while tunnelling. When sketching wave functions, students also show a shift in the axis of oscillation, as if the height of the axis of oscillation indicated the energy of the particle. We find inconsistencies between students' conceptual, mathematical, and graphical models of quantum tunnelling. As part of a curriculum in quantum physics, we have developed instructional materials to help students develop a more robust and less inconsistent picture of tunnelling, and present data suggesting that we have succeeded in doing so.Comment: Originally submitted to the European Journal of Physics on 2005 Feb 10. Pages: 14. References: 11. Figures: 9. Tables: 1. Resubmitted May 18 with revisions that include an appendix with the curriculum materials discussed in the paper (4 page small group UW-style tutorial

The intensity contrast of solar granulation: comparing Hinode SP results with MHD simulations

The contrast of granulation is an important quantity characterizing solar surface convection. We compare the intensity contrast at 630 nm, observed using the Spectro-Polarimeter (SP) aboard the Hinode satellite, with the 3D radiative MHD simulations of V{\"o}gler & Sch{\"u}ssler (2007). A synthetic image from the simulation is degraded using a theoretical point-spread function of the optical system, and by considering other important effects. The telescope aperture and the obscuration by the secondary mirror and its attachment spider, reduce the simulated contrast from 14.4 % to 8.5 %. A slight effective defocus of the instrument brings the simulated contrast down to 7.5 %, close to the observed value of 7.0 %. A proper consideration of the effects of the optical system and a slight defocus, lead to sufficient degradation of the synthetic image from the MHD simulation, such that the contrast reaches almost the observed value. The remaining small discrepancy can be ascribed to straylight and slight imperfections of the instrument, which are difficult to model. Hence, Hinode SP data are consistent with a granulation contrast which is predicted by 3D radiation MHD simulations.Comment: 5 pages, 4 figures, to be published in A&

Using resource graphs to represent conceptual change

We introduce resource graphs, a representation of linked ideas used when reasoning about specific contexts in physics. Our model is consistent with previous descriptions of resources and coordination classes. It can represent mesoscopic scales that are neither knowledge-in-pieces or large-scale concepts. We use resource graphs to describe several forms of conceptual change: incremental, cascade, wholesale, and dual construction. For each, we give evidence from the physics education research literature to show examples of each form of conceptual change. Where possible, we compare our representation to models used by other researchers. Building on our representation, we introduce a new form of conceptual change, differentiation, and suggest several experimental studies that would help understand the differences between reform-based curricula.Comment: 27 pages, 14 figures, no tables. Submitted for publication to the Physical Review Special Topics Physics Education Research on March 8, 200

Kerncraft: A Tool for Analytic Performance Modeling of Loop Kernels

Achieving optimal program performance requires deep insight into the interaction between hardware and software. For software developers without an in-depth background in computer architecture, understanding and fully utilizing modern architectures is close to impossible. Analytic loop performance modeling is a useful way to understand the relevant bottlenecks of code execution based on simple machine models. The Roofline Model and the Execution-Cache-Memory (ECM) model are proven approaches to performance modeling of loop nests. In comparison to the Roofline model, the ECM model can also describes the single-core performance and saturation behavior on a multicore chip. We give an introduction to the Roofline and ECM models, and to stencil performance modeling using layer conditions (LC). We then present Kerncraft, a tool that can automatically construct Roofline and ECM models for loop nests by performing the required code, data transfer, and LC analysis. The layer condition analysis allows to predict optimal spatial blocking factors for loop nests. Together with the models it enables an ab-initio estimate of the potential benefits of loop blocking optimizations and of useful block sizes. In cases where LC analysis is not easily possible, Kerncraft supports a cache simulator as a fallback option. Using a 25-point long-range stencil we demonstrate the usefulness and predictive power of the Kerncraft tool.Comment: 22 pages, 5 figure

Discrimination of Optical Coherent States using a Photon Number Resolving Detector

The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non-probabilistic state discrimination. We find that appropriate postselection of the measurement data of a photon number resolving detector can be used to discriminate two coherent states with small error probability. We compare our new receiver to an optimal intermediate measurement between minimum error discrimination and unambiguous state discrimination.Comment: 5 pages, 4 figure

Latitudinal variation of the solar photospheric intensity

We have examined images from the Precision Solar Photometric Telescope (PSPT) at the Mauna Loa Solar Observatory (MLSO) in search of latitudinal variation in the solar photospheric intensity. Along with the expected brightening of the solar activity belts, we have found a weak enhancement of the mean continuum intensity at polar latitudes (continuum intensity enhancement $\sim0.1 - 0.2$ corresponding to a brightness temperature enhancement of $\sim2.5{\rm K}$). This appears to be thermal in origin and not due to a polar accumulation of weak magnetic elements, with both the continuum and CaIIK intensity distributions shifted towards higher values with little change in shape from their mid-latitude distributions. Since the enhancement is of low spatial frequency and of very small amplitude it is difficult to separate from systematic instrumental and processing errors. We provide a thorough discussion of these and conclude that the measurement captures real solar latitudinal intensity variations.Comment: 24 pages, 8 figs, accepted in Ap

Graduate Quantum Mechanics Reform

We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey. We find that graduate students respond well to research-based techniques that have been tested mainly in introductory courses, and that they learn much of the new content introduced in each version of the course. We also find that students' ability to answer conceptual questions about graduate quantum mechanics is highly correlated with their ability to solve calculational problems on the same topics. In contrast, we find that students' understanding of basic undergraduate quantum mechanics concepts at the modern physics level is not improved by instruction at the graduate level.Comment: accepted to American Journal of Physic

Temporal evolution of headwall erosion rates derived from cosmogenic nuclide concentrations in the medial moraines of Glacier d'Otemma, Switzerland

Climate change affects the stability and erosion of high‐alpine rock walls above glaciers (headwalls) that deliver debris to glacier surfaces. Since supraglacial debris in the ablation zone alters the melt behaviour of the underlying ice, the responses of debris‐covered glaciers and of headwalls to climate change may be coupled. In this study, we analyse the beryllium‐10 (10Be)‐cosmogenic nuclide concentration history of glacial headwalls delivering debris to the Glacier d'Otemma in Switzerland. By systematic downglacier‐profile‐sampling of two parallel medial moraines, we assess changes in headwall erosion through time for small, well‐defined debris source areas. We compute apparent headwall erosion rates from 10Be concentrations ([10Be]), measured in 15 amalgamated medial moraine debris samples. To estimate both the additional 10Be production during glacial debris transport and the age of our samples we combine our field‐based data with a simple model that simulates downglacier debris trajectories. Furthermore, we evaluate additional grain size fractions for eight samples to test for stochastic mass wasting effects on [10Be]. Our results indicate that [10Be] along the medial moraines vary systematically with time and consistently for different grain sizes. [10Be] are higher for older debris, closer to the glacier terminus, and lower for younger debris, closer to the glacier head. Computed apparent headwall erosion rates vary between ~0.6 and 10.8 mm yr−1, increasing over a maximum time span of ~200 years towards the present. As ice cover retreats, newly exposed headwall surfaces may become susceptible to enhanced weathering and erosion, expand to lower elevations, and contribute formerly shielded bedrock of likely different [10Be]. Hence, we suggest that recently lower [10Be] reflect the deglaciation of the debris source areas since the end of the Little Ice Age