Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices

We study a disordered classical Heisenberg magnet with uniformly antiferromagnetic interactions which are frustrated on account of their long-range Coulomb form, {\em i.e.} $J(r)\sim -A\ln r$ in $d=2$ and $J(r)\sim A/r$ in $d=3$. This arises naturally as the $T\rightarrow 0$ limit of the emergent interactions between vacancy-induced degrees of freedom in a class of diluted Coulomb spin liquids (including the classical Heisenberg antiferromagnets on checkerboard, SCGO and pyrochlore lattices) and presents a novel variant of a disordered long-range spin Hamiltonian. Using detailed analytical and numerical studies we establish that this model exhibits a very broad paramagnetic regime that extends to very large values of $A$ in both $d=2$ and $d=3$. In $d=2$, using the lattice-Green function based finite-size regularization of the Coulomb potential (which corresponds naturally to the underlying low-temperature limit of the emergent interactions between orphan-spins), we only find evidence that freezing into a glassy state occurs in the limit of strong coupling, $A=\infty$, while no such transition seems to exist at all in $d=3$. We also demonstrate the presence and importance of screening for such a magnet. We analyse the spectrum of the Euclidean random matrices describing a Gaussian version of this problem, and identify a corresponding quantum mechanical scattering problem.Comment: two-column PRB format; 17 pages; 24 .eps figure

Analytic Framework for Students' Use of Mathematics in Upper-Division Physics

Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and researchers in characterizing students' difficulties with specific mathematical tools when solving the long and complex problems that are characteristic of upper-division. In this paper, we present this framework, including its motivation and development. We also describe an application of the framework to investigations of student difficulties with direct integration in electricity and magnetism (i.e., Coulomb's Law) and approximation methods in classical mechanics (i.e., Taylor series). These investigations provide examples of the types of difficulties encountered by advanced physics students, as well as the utility of the framework for both researchers and instructors.Comment: 17 pages, 4 figures, 3 tables, in Phys. Rev. - PE

Argon hollow cathode

An interest in alternate propellants for ion-bombardment thrusters, together with ground applications of this technology, has prompted consideration of argon. Several variations of conventional hollow cathode designs were tried, but the bulk of the testing used a hollow tube with an internal tungsten emitter and an orifice at one end. The optimum cathode tube diameter was found to be in the range of 1.0-2.5 cm, somewhat larger than those used for cesium and mercury. Optimum orifice diameter depended on operating conditions, and varied from 0.5 to 5 mm. Biasing the internal emitter negative relative to the cathode chamber reduced the external coupling voltage and should therefore improve orifice lifetime. The expected effect of this bias on emitter lifetime was less clear. Lifetime tests were not conducted as part of this investigation, but several designs show promise of long lifetime in specific applications

Some problems of the calculation of three-dimensional boundary layer flows on general configurations

An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations

Investigating teacher presence in courses using synchronous videoconferencing

This research examines teacher presence in high school distance courses that are delivered by synchronous videoconference. In rural and remote areas, many school districts are using videoconferencing as way to reach dispersed students. This collective case study uses mixed methods to unpack the notion of presence from the perspective of teachers and their students. This study reports four key findings which have implications for building presence in a videoconference course: teachers’ confidence and experience aligned with higher presence; teaching videoconference and face-to-face classes simultaneously led to challenges with developing presence; immediacy behaviors correlated with higher presence; and, students’ learning preference related to perceived teacher presence. These findings confirm many of the issues raised in the literature about technology integration but also contribute new perspectives on teaching presence in a videoconference

How periodic driving heats a disordered quantum spin chain

We study the energy absorption in real time of a disordered quantum spin chain subjected to coherent monochromatic periodic driving. We determine characteristic fingerprints of the well-known ergodic (Floquet-Eigenstate thermalization hypothesis for slow driving/weak disorder) and many-body localized (Floquet-many-body localization for fast driving/strong disorder) phases. In addition, we identify an intermediate regime, where the energy density of the system-unlike the entanglement entropy a local and bounded observable-grows logarithmically slowly over a very large time window

Complete Characterization of Quantum-Optical Processes

The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, i.e. classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.Comment: 5 pages, 4 figure