Interference between a large number of independent Bose-Einstein condensates

We study theoretically the interference patterns produced by the overlap of an array of Bose-Einstein condensates that have no phase coherence among them. We show that density-density correlations at different quasimomenta, which play an important role in two-condensate interference, become negligible for large $N$, where $N$ is the number of overlapping condensates. In order to understand the physics of this phenomenon, it is sufficient to consider the periodicity of the lattice and the statistical probability distribution of a random-walk problem. The average visibility of such interference patterns decreases as $N^{-1/2}$ for large $N$.Comment: 9 pages, 2 figure

The fierce urgency of now? Navigating paradoxes in sustainability education

This special section of the IJSHE brings together five papers originally presented at the fifth sustainability in higher education (SHE) conference, “The fierce urgency of now? Navigating Paradoxes in Sustainability Education,” hosted by Canterbury Christ Church, UK, in May 2020. Challenged by the words of Greta Thunberg spoken at the World Economic Forum in Davos in 2019, our aim was to provide a space to explore the role and responsibility of universities in a time of global crisis and to explore what it means to act as “if our house is on fire”. And then the Covid-19 pandemic struck […] and the focus we had planned took on new relevance. Under lockdown conditions, the conference (and HE more generally) had to move to an online format, and we all found ourselves working in unchartered territory. Although challenging, this opened up unexpected opportunities for colleagues and students from different institutions nationally and internationally to participate, increasing diversity and repositioning the SHE networks as more outward-facing. This apparent contradiction (that is, locking down, opportunities may be opened up) illustrates one of the many apparent paradoxes in the contemporary higher educational landscape

First exit times and residence times for discrete random walks on finite lattices

In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential landscape. We also compute quantities of interest for modelling surface reactions and other dynamic processes, such as the residence time in a subvolume, the joint residence time of several particles and the number of hits on a reflecting surface.Comment: 19 pages, 2 figure

Random walks on finite lattice tubes

Exact results are obtained for random walks on finite lattice tubes with a single source and absorbing lattice sites at the ends. Explicit formulae are derived for the absorption probabilities at the ends and for the expectations that a random walk will visit a particular lattice site before being absorbed. Results are obtained for lattice tubes of arbitrary size and each of the regular lattice types; square, triangular and honeycomb. The results include an adjustable parameter to model the effects of strain, such as surface curvature, on the surface diffusion. Results for the triangular lattice tubes and the honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag carbon nano-tubes with open ends.Comment: 22 pages, 4 figure

From Newton's Laws to the Wheeler-DeWitt Equation

This is a pedagogical paper which explains some ideas in cosmology at a level accessible to undergraduate students. It does not use general relativity, but uses the ideas of Newtonian cosmology worked out by Milne and McCrea. The cosmological constant is also introduced within a Newtonian framework. Following standard quantization procedures the Wheeler-DeWitt equation in the minisuperspace approximation is derived for empty and non-empty universes.Comment: 13 pages, 1 figur

Cosmological Inhomogeneities with Bose-Einstein Condensate Dark Matter

We consider the growth of cosmological perturbations to the energy density of dark matter during matter domination when dark matter is a scalar field that has undergone Bose-Einstein condensation. We study these inhomogeneities within the framework of both Newtonian gravity, where the calculation and results are more transparent, and General Relativity. The direction we take is to derive analytical expressions, which can be obtained in the small pressure limit. Throughout we compare our results to those of the standard cosmology, where dark matter is assumed pressureless, using our analytical expressions to showcase precise differences. We find, compared to the standard cosmology, that Bose-Einstein condensate dark matter leads to a scale factor, gravitational potential and density contrast that increase at faster rates.Comment: 17 pages, 2 figures; typos corrected, references adde

Black Holes with Weyl Charge and Non-Riemannian Waves

A simple modification to Einstein's theory of gravity in terms of a non-Riemannian connection is examined. A new tensor-variational approach yields field equations that possess a covariance similar to the gauge covariance of electromagnetism. These equations are shown to possess solutions analogous to those found in the Einstein-Maxwell system. In particular one finds gravi-electric and gravi-magnetic charges contributing to a spherically symmetric static Reissner-Nordstr\"om metric. Such Weyl ``charges'' provide a source for the non-Riemannian torsion and metric gradient fields instead of the electromagnetic field. The theory suggests that matter may be endowed with gravitational charges that couple to gravity in a manner analogous to electromagnetic couplings in an electromagnetic field. The nature of gravitational coupling to spinor matter in this theory is also investigated and a solution exhibiting a plane-symmetric gravitational metric wave coupled via non-Riemannian waves to a propagating spinor field is presented.Comment: 18 pages Plain Tex (No Figures), Classical and Quantum Gravit

Textures and Newtonian Gravity

Newtonian theory is used to study the gravitational effects of a texture, in particular the formation of massive structures.Comment: 4 pages, 4 ps figures, REVTEX, accepted for publication in PR

An Einstein-Hilbert Action for Axi-Dilaton Gravity in 4-Dimensions

We examine the axi-dilatonic sector of low energy string theory and demonstrate how the gravitational interactions involving the axion and dilaton fields may be derived from a geometrical action principle involving the curvature scalar associated with a non-Riemannian connection. In this geometry the antisymmetric tensor 3-form field determines the torsion of the connection on the frame bundle while the gradient of the metric is determined by the dilaton field. By expressing the theory in terms of the Levi-Civita connection associated with the metric in the ``Einstein frame'' we confirm that the field equations derived from the non-Riemannian Einstein-Hilbert action coincide with the axi-dilaton sector of the low energy effective action derived from string theory.Comment: 6 pages Plain Tex (No Figures), Letter to Editor Classical and Quantum Gravit

Descriptive Analysis of a Baseline Concussion Battery Among U.S. Service Academy Members: Results from the Concussion Assessment, Research, and Education (CARE) Consortium

Introduction The prevalence and possible long-term consequences of concussion remain an increasing concern to the U.S. military, particularly as it pertains to maintaining a medically ready force. Baseline testing is being used both in the civilian and military domains to assess concussion injury and recovery. Accurate interpretation of these baseline assessments requires one to consider other influencing factors not related to concussion. To date, there is limited understanding, especially within the military, of what factors influence normative test performance. Given the significant physical and mental demands placed on service academy members (SAM), and their relatively high risk for concussion, it is important to describe demographics and normative profile of SAMs. Furthermore, the absence of available baseline normative data on female and non-varsity SAMs makes interpretation of post-injury assessments challenging. Understanding how individuals perform at baseline, given their unique individual characteristics (e.g., concussion history, sex, competition level), will inform post-concussion assessment and management. Thus, the primary aim of this manuscript is to characterize the SAM population and determine normative values on a concussion baseline testing battery. Materials and Methods All data were collected as part of the Concussion Assessment, Research and Education (CARE) Consortium. The baseline test battery included a post-concussion symptom checklist (Sport Concussion Assessment Tool (SCAT), psychological health screening inventory (Brief Symptom Inventory (BSI-18) and neurocognitive evaluation (ImPACT), Balance Error Scoring System (BESS), and Standardized Assessment of Concussion (SAC). Linear regression models were used to examine differences across sexes, competition levels, and varsity contact levels while controlling for academy, freshman status, race, and previous concussion. Zero inflated negative binomial models estimated symptom scores due to the high frequency of zero scores. Results Significant, but small, sex effects were observed on the ImPACT visual memory task. While, females performed worse than males (p < 0.0001, pη2 = 0.01), these differences were small and not larger than the effects of the covariates. A similar pattern was observed for competition level on the SAC. There was a small, but significant difference across competition level. SAMs participating in varsity athletics did significantly worse on the SAC compared to SAMs participating in club or intramural athletics (all p’s < 0.001, η2 = 0.01). When examining symptom reporting, males were more than two times as likely to report zero symptoms on the SCAT or BSI-18. Intramural SAMs had the highest number of symptoms and severity compared to varsity SAMs (p < 0.0001, Cohen’s d < 0.2). Contact level was not associated with SCAT or BSI-18 symptoms among varsity SAMs. Notably, the significant differences across competition level on SCAT and BSI-18 were sub-clinical and had small effect sizes. Conclusion The current analyses provide the first baseline concussion battery normative data among SAMs. While statistically significant differences may be observed on baseline tests, the effect sizes for competition and contact levels are very small, indicating that differences are likely not clinically meaningful at baseline. Identifying baseline differences and significant covariates is important for future concussion-related analyses to inform concussion evaluations for all athlete levels