Boundary-induced violation of the Dirac fermion parity and its signatures in local and global tunneling spectra of graphene

Extended defects in graphene, such as linear edges, break the translational invariance and can also have an impact on the symmetries specific to massless Dirac-like quasiparticles in this material. The paper examines the consequences of a broken Dirac fermion parity in the framework of the effective boundary conditions varying from the Berry-Mondragon mass confinement to a zigzag edge. The parity breaking reflects the structural sublattice asymmetry of zigzag-type edges and is closely related to the previously predicted time-reversal symmetric edge states. We calculate the local and global densities of the edge states and show that they carry a specific polarization, resembling, to some extent, that of spin-polarized materials. The lack of the parity leads to a nonanalytical particle-hole asymmetry in the edge-state properties. We use our findings to interpret recently observed tunneling spectra in zigzag-terminated graphene. We also propose a graphene-based tunneling device where the particle-hole asymmetric edge states result in a strongly nonlinear conductance-voltage characteristics, which could be used to manipulate the tunneling transport.Comment: 8 pages, 5 figures, to be published in Phys. Rev.

Light Scattering by Cholesteric Skyrmions

We study the light scattering by localized quasi planar excitations of a Cholesteric Liquid Crystal known as spherulites. Due to the anisotropic optical properties of the medium and the peculiar shape of the excitations, we quantitatively evaluate the cross section of the axis-rotation of polarized light. Because of the complexity of the system under consideration, first we give a simplified, but analytical, description of the spherulite and we compare the Born approximation results in this setting with those obtained by resorting to a numerical exact solution. The effects of changing values of the driving external static electric (or magnetic) field is considered. Possible applications of the phenomenon are envisaged.Comment: 18 pages, 14 figure

Orthogonality catastrophe and Kondo effect in graphene

Anderson's orthogonality catastrophe in graphene, at energies close to the Dirac point, is analyzed. It is shown that, in clean systems, the orthogonality catastrophe is suppressed, due to the vanishing density of states at the Dirac point. In the presence of preexisting localized states at the Dirac energy, the orthogonality catastrophe shows similar features to those found in normal metals with a finite density of states at the Fermi level. The implications for the Kondo effect induced by magnetic impurities, and for the Fermi edge singularities in tunneling processes are also discussed.Comment: 7 pages, 7 figure

Unfolding symmetric Bogdanov-Takens bifurcations for front dynamics in a reaction-diffusion system

This manuscript extends the analysis of a much studied singularly perturbed three-component reaction-diffusion system for front dynamics in the regime where the essential spectrum is close to the origin. We confirm a conjecture from a preceding paper by proving that the triple multiplicity of the zero eigenvalue gives a Jordan chain of length three. Moreover, we simplify the center manifold reduction and computation of the normal form coefficients by using the Evans function for the eigenvalues. Finally, we prove the unfolding of a Bogdanov-Takens bifurcation with symmetry in the model. This leads to stable periodic front motion, including stable traveling breathers, and these results are illustrated by numerical computations.Comment: 39 pages, 7 figure

Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals

Quasi-bound states in an open system do in general not form an orthogonal and complete basis. It is, however, expected that the non-orthogonality is weak in the case of well-confined states except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the non-orthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly non-orthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenomenon is related to the asymmetric scattering between clockwise and counterclockwise propagating waves in the spiral geometry. Numerical simulations of ray dynamics reveal a clear ray-wave correspondence.Comment: 8 pages, 10 figure

Analyzing the Relationship between Senior High School Teachers’ Extent of Application of the Linguistic Intelligence and the Student Motivation in the Classroom

The study aimed to analyze the relationship between senior high school teachers’ extent of application of the Linguistic Intelligence theory and their perception regarding student motivation in the classroom.The motivation of the study focuses on how the linguistic intelligence affects the delivery of instruction and the possible teaching technique and innovation for the teachers. The study used the descriptive-correlational method of research, and Kendall Tau b was used to establish the connection for the interpretation and implications of such findings. It is discovered that teachers' levels of perception about student motivation, their levels of self-efficacy for motivating students, and the strategies they employ in the classroom are significantly and directly related to the extent to which they apply the linguistic intelligence theory in the classroom. Additionally, there was a substantial and direct correlation between their level of perception of student motivation, their level of self-efficacy in inspiring students, and the methods they employ in the classroom. This research implies that teachers employ tactics and seek to coordinate their work with the factors they believe motivate their students. A study on the effects of technology on linguistic intelligenceand other Multiple Intelligence procedures might be carried out to assist teachers in bettering their comprehension of their student

The Practice of Gardner’s Multiple Intelligences Theory in the Classroom

The study attempted to determine the practices of Gardner’s Multiple Intelligences Theory in the classroom. It also determined the level of awareness of the senior high school teachers and students of Gardner’s Multiple Intelligences Theory, the extent of practice and the relationship between the perceived extent of practice of Gardner’s Multiple Intelligence Theory and their profile and level of awareness. The descriptive-correlational method of research was employed in the study and Kendall Tau b was utilized to determine the relationship for interpretation and implication of such findings. Result shows that the senior-high school teachers were adequately familiar with Gardner’s Multiple Intelligences (GMI) theories and the teachers themselves and their students generally agreed that all these eight (8) multiple intelligences were applied and frequently practiced in the classroom. The findings of the study also indicated that there were significant associations between the age, gender, specialization and highest educational attainment and the extent of some practices of the GMI theories in the classroom. It can be noted that as the senior high school teachers grow in age, the less likely they will use visual aids in class such as maps, charts, and diagrams and give students the opportunity to use drama, dance, or physical activity as a part of their learning process. LGBT teachers will tend to become more effective in reading or lecturing to the class and in encouraging students to peer tutor or help each other in class. Language education specialists will have a higher inclination to encourage students to employ their verbal skills to communicate, solve problems, and express inner feelings. Moreover, the higher the educational attainment of the teachers, the less likely they will use visual presentations during class (e.g., write on chalkboard, use overhead projector) and encourage students to visually represent the concepts being taught/ discussed. It is recommended that the senior high school classroom teachers are enjoined to continuously apply MI theories in their teaching practices. This means self-development through reading, studying, and learning more about not only Gardner’s theory but other theory-based practices. In addition, teachers at the high school level need to have more resources in their practice of multiple intelligence theories put in place in order to support their abilities to properly educate and motivate students to sustain their education

Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy

The Abelian Chern-Simons Gauge Field Theory in 2+1 dimensions and its relation with holomorphic Burgers' Hierarchy is considered. It is shown that the relation between complex potential and the complex gauge field as in incompressible and irrotational hydrodynamics, has meaning of the analytic Cole-Hopf transformation, linearizing the Burgers Hierarchy in terms of the holomorphic Schr\"odinger Hierarchy. Then the motion of planar vortices in Chern-Simons theory, appearing as pole singularities of the gauge field, corresponds to motion of zeroes of the hierarchy. Using boost transformations of the complex Galilean group of the hierarchy, a rich set of exact solutions, describing integrable dynamics of planar vortices and vortex lattices in terms of the generalized Kampe de Feriet and Hermite polynomials is constructed. The results are applied to the holomorphic reduction of the Ishimori model and the corresponding hierarchy, describing dynamics of magnetic vortices and corresponding lattices in terms of complexified Calogero-Moser models. Corrections on two vortex dynamics from the Moyal space-time non-commutativity in terms of Airy functions are found.Comment: 15 pages, talk presented in Workshop `Nonlinear Physics IV: Theory and Experiment`, 22-30 June 2006, Gallipoli, Ital

Motivating social distancing during the Covid-19 pandemic: An online experiment. ESRI Working Paper No. 658 April 2020

Social distancing during the COVID-19 pandemic will save lives. We tested communication strategies to promote social distancing via an online experiment (N = 500) commissioned by Ireland’s Department of Health. A control group saw a current informational poster. Two treatment groups saw similar posters with messages that highlighted: (i) the risk of transmission to identifiable persons vulnerable to COVID-19; (ii) the exponential nature of transmission. We then measured judgements of behaviours previously identified by focus groups as “marginal” (meaning that people were not sure whether they were advisable, such meeting others outdoors, or visiting parents). We recorded intention to undertake behaviours and stated acceptability of behaviours. Our hypotheses, that both treatments would increase participants’ caution about marginal behaviours, were preregistered (i.e. lodged with an international organisation for open science before data collection). Results confirmed the hypotheses. The findings suggest that the thought of infecting vulnerable people or large numbers of people can motivate social distancing. This has implications for communications strategies. The stud