Rigidity and Normal Modes in Random Matrix Spectra

We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is linear, and for large matrices, the normal modes are found to be Chebyshev polynomials of the second kind. We contrast this with the behaviour of a sequence of uncorrelated levels, which has a quadratic normal mode spectrum. The difference in the rigidity of random matrix spectra and sequences of uncorrelated levels can be attributed to this difference in the normal mode spectra. We illustrate this by calculating the number variance in the two cases.Comment: 12 pages, 1 LaTeX fil

Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, $(0,s)$, containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe

A Framework for the Landscape

It seems likely that string theory has a landscape of vacua that includes very many metastable de Sitter spaces. However, as emphasized by Banks, Dine and Gorbatov, no current framework exists for examining these metastable vacua in string theory. In this paper we attempt to correct this situation by introducing an eternally inflating background in which the entire collection of accelerating cosmologies is present as intermediate states. The background is a classical solution which consists of a bubble of zero cosmological constant inside de Sitter space, separated by a domain wall. At early and late times the flat space region becomes infinitely big, so an S-matrix can be defined. Quantum mechanically, the system can tunnel to an intermediate state which is pure de Sitter space. We present evidence that a string theory S-matrix makes sense in this background and contains metastable de Sitter space as an intermediate state.Comment: 29+13 pages, 25 figures; v2: minor corrections, references adde

There’s just huge anxiety: ontological security, moral panic, and the decline in young people’s mental health and well-being in the UK

This study aims to critically discuss factors associated with a recent dramatic rise in recorded mental health issues amongst UK youth. It draws from interviews and focus groups undertaken with young people, parents and professionals. We offer valuable new insights into significant issues affecting young people’s mental health and well-being that are grounded in their lived experiences and in those who care for and work with them. By means of a thematic analysis of the data, we identified an increase in anxiety related to: future orientation, social media use, education, austerity, and normalization of mental distress and self-harm. We apply the notion of ontological security in our interpretation of how socio-cultural and political changes have increased anxiety amongst young people and consequent uncertainty about the self, the world and the future, leading to mental health problems. There are also problems conceptualizing and managing adolescent mental health, including increased awareness, increased acceptance of these problems, and stigmatisation. We relate this to the tendency for moral panic and widespread dissemination of problems in a risk society. In our conclusion, we highlight implications for future research, policy and practice

The reported use and effectiveness of Hypericum (St John’s wort) on affective symptoms in a depression self-help group

A recent meta-analysis suggested that Hypericum perforatum (St John’s wort) is an effective treatment for mild to moderate depression and may have a superior side-effect profile to some antidepressant drugs. The aim of this study was to assess the use of herbal remedies in treating depressive and anxiety symptoms, as reported by members of the UK self-help organization Depression Alliance using self-completed questionnaires. More than 50% of the 452 respondents reported using Hypericum, onequarter of whom also reported concurrent use of traditional antidepressants. Most of the sample reported sufficient symptoms for warranting a diagnosis of major depression, with the majority also describing symptoms suggestive of co-morbid psychiatric conditions. One-half of the Hypericum users experienced symptom improvement, which for most occurred within the first 4 weeks of use. Response was better for those with mild as compared to severe symptoms and poorer for those taking Hypericum alongside other antidepressants. The responders were generally older than non-responders. Adverse effects were reported by one-quarter of users and were mostly psychological in nature. This retrospective survey indicated that use of herbal remedies was common in this population. Although often helpful in relieving symptoms, particularly in those with mild depression, there is a risk of adverse events and drug interaction

Dirac monopole with Feynman brackets

We introduce the magnetic angular momentum as a consequence of the structure of the sO(3) Lie algebra defined by the Feynman brackets. The Poincare momentum and Dirac magnetic monopole appears as a direct result of this framework.Comment: 10 page

Momentum relaxation due to polar optical phonons in AlGaN/GaN heterostructures

Using the dielectric continuum (DC) model, momentum relaxation rates are calculated for electrons confined in quasi-two-dimensional (quasi-2D) channels of AlGaN/GaN heterostructures. Particular attention is paid to the effects of half-space and interface modes on the momentum relaxation. The total momentum relaxation rates are compared with those evaluated by the three-dimensional phonon (3DP) model, and also with the Callen results for bulk GaN. In heterostructures with a wide channel (effective channel width >100 Å), the DC and 3DP models yield very close momentum relaxation rates. Only for narrow-channel heterostructures do interface phonons become important in momentum relaxation processes, and an abrupt threshold occurs for emission of interface as well as half-space phonons. For a 30-Å GaN channel, for instance, the 3DP model is found to underestimate rates just below the bulk phonon energy by 70% and overestimate rates just above the bulk phonon energy by 40% compared to the DC model. Owing to the rapid decrease in the electron-phonon interaction with the phonon wave vector, negative momentum relaxation rates are predicted for interface phonon absorption in usual GaN channels. The total rates remain positive due to the dominant half-space phonon scattering. The quasi-2D rates can have substantially higher peak values than the three-dimensional rates near the phonon emission threshold. Analytical expressions for momentum relaxation rates are obtained in the extreme quantum limits (i.e., the threshold emission and the near subband-bottom absorption). All the results are well explained in terms of electron and phonon densities of states

Hot electron energy relaxation in lattice-matched InAlN/AlN/GaN heterostructures: The sum rules for electron-phonon interactions and hot-phonon effect

Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation and energy relaxation time due to both half-space and interface phonons are calculated as functions of the electron temperature Te using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: with no hot phonons or screening the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for energy relaxation time with the two phonon models (within a 5% of deviation). However the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the power dissipation values obtained from the DC and 3DP models are in general different in the pure phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register’s scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the energy relaxation: their contribution is enhanced in the pure emission process but is dramatically reduced after including the HPE. Our calculation with both phonon models has obtained a great fall in energy relaxation time at low electron temperatures (Te < 750 K) and slow decrease at the high temperatures with the use of decreasing phonon lifetime with Te. The calculated temperature dependence of the relaxation time and the high-temperature relaxation time ∼0.09 ps are in good agreement with experimental results

Action research in physical education: focusing beyond myself through cooperative learning

This paper reports on the pedagogical changes that I experienced as a teacher engaged in an action research project in which I designed and implemented an indirect, developmentally appropriate and child‐centred approach to my teaching. There have been repeated calls to expunge – or at least rationalise – the use of traditional, teacher‐led practice in physical education. Yet despite the advocacy of many leading academics there is little evidence that such a change of approach is occurring. In my role as teacher‐as‐researcher I sought to implement a new pedagogical approach, in the form of cooperative learning, and bring about a positive change in the form of enhanced pupil learning. Data collection included a reflective journal, post‐teaching reflective analysis, pupil questionnaires, student interviews, document analysis, and non‐participant observations. The research team analysed the data using inductive analysis and constant comparison. Six themes emerged from the data: teaching and learning, reflections on cooperation, performance, time, teacher change, and social interaction. The paper argues that cooperative learning allowed me to place social and academic learning goals on an even footing, which in turn placed a focus on pupils’ understanding and improvement of skills in athletics alongside their interpersonal development

The tails in the Helix Nebula NGC 7293

We have examined a stream-source model for the production of the cometary tails observed in the Helix Nebula NGC 7293 in which a transonic or moderately supersonic stream of ionized gas overruns a source of ionized gas. Hydrodynamic calculations reveal velocity structures which are in good agreement with the observational data on tail velocities and are consistent with observations of the nebular structure. The results also are indicative of a stellar atmosphere origin for the cometary globules. Tail remnants persist for timescales long enough for their identification with faint striations visible in the nebula gas to be plausible.Comment: 7 pages, 6 figures, accepted for publication in A&