Quantum symmetries and the Weyl-Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase-space. Each such phase-space representation is a Weyl-Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by `factorising' the Weyl-Wigner product. However, not every real, unitary representation on phase-space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl-Wigner product and can be factorised. The conditions under which this is possible are examined. Examples are presented.Comment: Latex2e file, 37 page

Non-positivity of the Wigner function and bounds on associated integrals

The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval [0,1]. The problem of finding best-possible upper and lower bounds for a given region is the problem of finding the greatest and least eigenvalues of an associated Hermitian operator. Exactly solvable examples are described, and possible extensions are indicated.Comment: 5 pages, Latex2e fil

The effect of cultural background on metaphor interpretation

This article describes a study that investigated the ways in which Bangladeshi students interpreted metaphors used by their lecturers during a short course at a British university. The students were asked to interpret a number of metaphors presented in context. They were also asked to identify the value judgements that were being expressed through these metaphors in these particular contexts. Culture-specific assumptions about the target domains appeared to affect the students’ recognition of the lecturers’ attitudes to the issues they were discussing. In order to identify areas of disparity between the (working) cultures of the Bangladeshi students and their British lecturers, Hofstede’s (1980) cultural values questionnaire was administered. The students were found to be more likely than their lecturers to favour uncertainty avoidance, and to favour high power distance at work. The kinds of (mis)interpretations that the students made of (the evaluative content of) the metaphors appeared in accordance with these cultural differences. Implications of these findings are discussed

Oscillating-flow regenerator test rig: Woven screen and metal felt results

We present correlating expressions, in terms of Reynolds or Peclet numbers, for friction factors, Nusselt numbers, enhanced axial conduction ratios, and overall heat flux ratios in four porous regenerator samples representative of stirling cycle regenerators: two woven screen samples and two random wire samples. Error estimates and comparison of data with others suggest our correlations are reliable, but we need to test more samples over a range of porosities before our results will become generally useful

The great outdoors: how a green exercise environment can benefit all

The studies of human and environment interactions usually consider the extremes of environment on individuals or how humans affect the environment. It is well known that physical activity improves both physiological and psychological well-being, but further evidence is required to ascertain how different environments influence and shape health. This review considers the declining levels of physical activity, particularly in the Western world, and how the environment may help motivate and facilitate physical activity. It also addresses the additional physiological and mental health benefits that appear to occur when exercise is performed in an outdoor environment. However, people's connectedness to nature appears to be changing and this has important implications as to how humans are now interacting with nature. Barriers exist, and it is important that these are considered when discussing how to make exercise in the outdoors accessible and beneficial for all. The synergistic combination of exercise and exposure to nature and thus the 'great outdoors' could be used as a powerful tool to help fight the growing incidence of both physical inactivity and non-communicable disease. © 2013 Gladwell et al.; licensee BioMed Central Ltd

Reverse engineering a spectrum: using fluorescent spectra of molecular hydrogen to recreate the missing Lyman-α line of pre-main sequence stars

The hydrogen Lyman-α (Lyα) line, a major source of ionization of metals in the circumstellar disks of pre-main sequence (PMS) stars, is usually not observed due to absorption by interstellar and circumstellar hydrogen. We have developed a technique to reconstruct the intrinsic Lyα line using the observed emission in the H2 B-X lines that are fluoresced by Lyα. We describe this technique and the subsequent analysis of the ultraviolet (UV) spectra of the TW Hya, RU Lupi and other PMS stars. We find that the reconstructed Lyα lines are indeed far brighter than any other feature in the UV spectra of these stars and therefore play an important role in the ionization and heating of the outer layers of circumstellar disks