Computing as the 4th “R”: a general education approach to computing education

Computing and computation are increasingly pervading our lives, careers, and societies - a change driving interest in computing education at the secondary level. But what should define a "general education" computing course at this level? That is, what would you want every person to know, assuming they never take another computing course? We identify possible outcomes for such a course through the experience of designing and implementing a general education university course utilizing best-practice pedagogies. Though we nominally taught programming, the design of the course led students to report gaining core, transferable skills and the confidence to employ them in their future. We discuss how various aspects of the course likely contributed to these gains. Finally, we encourage the community to embrace the challenge of teaching general education computing in contrast to and in conjunction with existing curricula designed primarily to interest students in the field

Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these models, have an interesting multiplicity structure. The results are obtained via a decomposition of the Laplacian into a direct sum of Jacobi matrices

Spectrum in the broken phase of a λϕ4\lambda\phi^4 theory

We derive the spectrum in the broken phase of a $\lambda\phi^4$ theory, in the limit $\lambda\to\infty$, showing that this goes as even integers of a renormalized mass in agreement with recent lattice computations.Comment: 4 pages, 1 figure. Accepted for publication in International Journal of Modern Physics

Critical Behavior of Coupled q-state Potts Models under Weak Disorder

We investigate the effect of weak disorder on different coupled $q$-state Potts models with $q\le 4$ using two loops renormalisation group. This study presents new examples of first order transitions driven by randomness. We found that weak disorder makes the models decouple. Therefore, it appears that no relations emerge, at a perturbation level, between the disordered $q_1\times q_2$-state Potts model and the two disordered $q_1$, $q_2$-state Potts models ($q_1\ne q_2$), despite their central charges are similar according to recent numerical investigations. Nevertheless, when two $q$-state Potts models are considered ($q>2$), the system remains always driven in a strong coupling regime, violating apparently the Imry-Wortis argument.Comment: 7 pages + 1 PS figure (Latex

Green functions and nonlinear systems: Short time expansion

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with numerical results. The relevance of these results relies on the possibility of fully exploiting a gradient expansion in both classical and quantum field theory granting the existence of a strong coupling expansion. Having a Green function in this regime in quantum field theory amounts to obtain the corresponding spectrum of the theory.Comment: 7 pages, 3 figures. Version accepted for publication in International Journal of Modern Physics

Bulk-edge coupling in the non-abelian ν=5/2\nu=5/2 quantum Hall interferometer

Recent schemes for experimentally probing non-abelian statistics in the quantum Hall effect are based on geometries where current-carrying quasiparticles flow along edges that encircle bulk quasiparticles, which are localized. Here we consider one such scheme, the Fabry-Perot interferometer, and analyze how its interference patterns are affected by a coupling that allows tunneling of neutral Majorana fermions between the bulk and edge. While at weak coupling this tunneling degrades the interference signal, we find that at strong coupling, the bulk quasiparticle becomes essentially absorbed by the edge and the intereference signal is fully restored.Comment: 5 pages, 1 figur

On the existence of impurity bound excitons in one-dimensional systems with zero range interactions

We consider a three-body one-dimensional Schr\"odinger operator with zero range potentials, which models a positive impurity with charge $\kappa > 0$ interacting with an exciton. We study the existence of discrete eigenvalues as $\kappa$ is varied. On one hand, we show that for sufficiently small $\kappa$ there exists a unique bound state whose binding energy behaves like $\kappa^4$, and we explicitly compute its leading coefficient. On the other hand, if $\kappa$ is larger than some critical value then the system has no bound states