Dynamics of localized waves in 1D random potentials: statistical theory of the coherent forward scattering peak

As recently discovered [PRL ${\bf 109}$ 190601(2012)], Anderson localization in a bulk disordered system triggers the emergence of a coherent forward scattering (CFS) peak in momentum space, which twins the well-known coherent backscattering (CBS) peak observed in weak localization experiments. Going beyond the perturbative regime, we address here the long-time dynamics of the CFS peak in a 1D random system and we relate this novel interference effect to the statistical properties of the eigenfunctions and eigenspectrum of the corresponding random Hamiltonian. Our numerical results show that the dynamics of the CFS peak is governed by the logarithmic level repulsion between localized states, with a time scale that is, with good accuracy, twice the Heisenberg time. This is in perfect agreement with recent findings based on the nonlinear $\sigma$-model. In the stationary regime, the width of the CFS peak in momentum space is inversely proportional to the localization length, reflecting the exponential decay of the eigenfunctions in real space, while its height is exactly twice the background, reflecting the Poisson statistical properties of the eigenfunctions. Our results should be easily extended to higher dimensional systems and other symmetry classes.Comment: See the published article for the updated versio

Momentum-space dynamics of Dirac quasiparticles in correlated random potentials: Interplay between dynamical and Berry phases

We consider Dirac quasi-particles, as realized with cold atoms loaded in a honeycomb lattice or in a $\pi$-flux square lattice, in the presence of a weak correlated disorder such that the disorder fluctuations do not couple the two Dirac points of the lattices. We numerically and theoretically investigate the time evolution of the momentum distribution of such quasi-particles when they are initially prepared in a quasi-monochromatic wave packet with a given mean momentum. The parallel transport of the pseudo-spin degree of freedom along scattering paths in momentum space generates a geometrical phase which alters the interference associated with reciprocal scattering paths. In the massless case, a well-known dip in the momentum distribution develops at backscattering (respective to the Dirac point considered) around the transport mean free time. This dip later vanishes in the honeycomb case because of trigonal warping. In the massive case, the dynamical phase of the scattering paths becomes crucial. Its interplay with the geometrical phase induces an additional transient broken reflection symmetry in the momentum distribution. The direction of this asymmetry is a property of the Dirac point considered, independent of the energy of the wave packet. These Berry phase effects could be observed in current cold atom lattice experiments.Comment: Additional data and explanations compared to version 1. See published article for the latest versio

Analytical and numerical study of uncorrelated disorder on a honeycomb lattice

We consider a tight-binding model on the regular honeycomb lattice with uncorrelated on-site disorder. We use two independent methods (recursive Green's function and self-consistent Born approximation) to extract the scattering mean free path, the scattering mean free time, the density of states and the localization length as a function of the disorder strength. The two methods give excellent quantitative agreement for these single-particle properties. Furthermore, a finite-size scaling analysis reveals that all localization lengths for different lattice sizes and different energies (including the energy at the Dirac points) collapse onto a single curve, in agreement with the one-parameter scaling theory of localization. The predictions of the self-consistent theory of localization however fail to quantitatively reproduce these numerically-extracted localization lengths.Comment: 19 pages, 25 figure

Learning english language with technology : case study of a primary school in Kota Belud, Sabah

Teaching English language in primary school using ICT technology is a great challenge for language teachers. The study investigates how 40 voluntary student teachers of a public university in Sabah use ICT and multisensory approach to teach English. The study employs The Learner Centric Ecology of Resources Framework (Luckin, 2008) as a guide to observe knowledge scaffolding of students learning. Focus group interviews to elicite qualitative data were done with some selected student teachers who participated in the voluntary teaching job at selected primary school in Kota Belud, Sabah. The results showed that the majority of the student teachers were motivated to teach English using multisensory approach because it helped them to connect English with outside world via visual aids (multimedia). The student teachers’ reflective journals also indicated that they were able to align the ICT materials with the proficiency level of the students, create interactive teaching and learning materials, using ICT to improve class control because the graphics and sounds attracted students’ attention. All the actions by the student teachers proved that they were frequently updating each other in teaching like how the Luckin’s framework suggested. If this method of learning is practiced by more schools, it would make language learning interesting