Equilibration of Quantum Gases

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators and correlation functions. We show that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists of N fermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time O(1/N).Comment: 9 + 10 pages, 5 figures; v2 is expanded to include extended results involving local equilibration on lattice systems, together with new examples and minor improvement

Imagining 'environment' in sustainable development

The paper presents an argument for a broader and more complex definition of environment than that currently offered in sustainable development discourse and practice. Sustainable development is rooted in dominant western rational and instrumental scientific representations of human-environment relationships. As such, it has been criticised as misrepresentative and meaningless for many of those for whom it is intended. Recent contributions by social scientists have emphasized the need to move beyond the narrow construction of the human-environment dichotomy found in western scientific rhetoric. These emerging ‘new ecologies’ advocate a re-imagining of human-environment relationships as holistic, connective, and relational, and as a product of direct perception and active engagement in the world. The Boumā National Heritage Park, Fiji, a community-based ecotourism initiative is presented as a case study to identify discrepancies between indigenous perceptions of the environment and those of formally educated western development practitioners, as well as the potential for ongoing convergence

Production of trans-Neptunian binaries through chaos-assisted capture

The recent discovery of binary objects in the Kuiper-belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary-object formation model based on the notion of chaos-assisted capture. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity, and orbital element distribu- tions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering in the circular Hill four-body problem and find that the chaos-assisted capture mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the 'fine-tuning' problem recently identified by Noll et al. (2007) is also addressed.Comment: submitted to MNRA

An Ethnography of Entanglements: Mercury’s Presence and Absence in Artisanal and Small-scale Gold-mining in Antioquia, Colombia

This paper describes a ‘follow the thing’ methodology as applied to an ethnography of entanglements. This methodology allowed for a materially and politically nuanced understanding of Antioquia, Colombia’s response to mercury pollution. This pollution primarily originates from the Artisanal and Small-Scale Gold Mining (ASGM) industry where mercury is employed in the gold extraction process. In following the mercury, the authors experiment with an ethnography of entanglements. The paper discusses how they address the current lacunae in mining ethnographies by focussing on mining as ‘practice’, going past the provision of technical descriptions of mining and ethnographic descriptions of miners to an ethnography of mining. This ethnographic approach considers the politics of materiality and addresses a lack of attention to the impacts of the presence and absence of materials on social life. Various mining practices in Antioquia illuminate how entanglements between miners and mercury have been co-constitutive of particular modes of ASGM. The paper will also provide examples of ‘negative mercury entanglements’ where efforts have been made to extricate mercury from mining practices. Rather than creating a vacuum, these mercury absences have been generative of new contested symbolic and material arrangements including entrepreneurial and ‘responsible’ mining, debates over miners’ rights, and the creation of new political relationships between ASGM and large-scale mining companies.fals

A Collaborative Approach: Two Perspectives

This article is a story of collaboration between a principal, Baek Chong, and the mathematics coach, Megan Farrelly. This article shows both perspectives: Baek\u27s thoughts are written in regular typeface, whereas Megan\u27s perspective is italicized. Both educators work at Mark Twain Middle School in Fairfax County Public Schools in Virginia which has nearly 900 seventh- and eighth-grade students. Twain Middle School serves a diverse population, of which about 35% of the students arc on free or reduced lunch, 15% receive special education services, 14% receive English language services, and 40% of the students are in the advanced academics program