Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Primary to secondary LOTE articulation: A local case in Australia

In this study of articulation issues related to languages other than English (LOTE), "articulation" is defined and the challenges surrounding it are overviewed. Data taken from an independent school's admission documents over a 4-year period provide insights and reveal trends concerning students' preferences for language study, LOTE study continuity, and reasons for LOTE selection. The data also provides an accounting of some multiple LOTE learning experiences. The analysis indicates that many students who begin a LOTE in the early grades are thwarted in becoming proficient, because (1) continuation in the language is impossible due to unavailability of instruction; (2) expanded learning is hampered by teachers' inability to deal with a range of learners, (3) extended learning is hampered by administrative decisions or policies, or (4) students lose interest in the first LOTE and switch to another. Finally, a call is made for data gathering and research in local contexts to gain a better understanding of LOTE articulation challenges at the local, state, national, and international levels.