Geometry of Deformed Boson Algebras

Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding deformed oscillators are provided. The deformation parameters are identified with coefficients of non-linear terms in the normal forms expansion of a family of classical Hamiltonian systems. These quantum deformations are trivial in the sense that they correspond to non-unitary transformations of the Weyl algebra. They are non-trivial in the sense that the deformed commutators consistently quantise a class of non-canonical classical Poisson structures.Comment: 20 pages, late

Quantisation on the Two-Handled Sphere

この論文は国立情報学研究所の電子図書館事業により電子化されました。研究会報告There is a class of polygonal billiards which can be mapped into classical flows on the surface of a g-handled sphere. In particular the π/3-rhombus billiard flow is equivalent to a flow on the surface of a two-handled sphere. The quantisation of this system is as yet an unsolved problem

Semiclassical transmission across transition states

It is shown that the probability of quantum-mechanical transmission across a phase space bottleneck can be compactly approximated using an operator derived from a complex Poincar\'e return map. This result uniformly incorporates tunnelling effects with classically-allowed transmission and generalises a result previously derived for a classically small region of phase space.Comment: To appear in Nonlinearit

Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems

Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because another formulation can be given to unitary perturbation theory. When worked out for quantum spin systems, this variant is found to be formally equivalent to canonical perturbation theory applied to nearly integrable systems consisting of classical spins. In particular, it becomes possible to locate the quantum-mechanical operator-valued equivalent of the frequency denominators that may cause divergence of the classical perturbation series. The results that are established here link the concept of quantum-mechanical integrability to a technical question, namely, the behavior of specific perturbation series

Talking South African fathers: a critical examination of men’s constructions and experiences of fatherhood and fatherlessness

The absence of biological fathers in South Africa has been constructed as a problem for children of both sexes but more so for boy-children. Arguably the dominant discourse in this respect has demonized non-nuclear, female-headed households. Fathers are constructed as either absent or ‘bad’. Thus it has become important to explore more closely how male care-givers have been experienced by groups of men in South Africa. This article examines discourses of fatherhood and fatherlessness by drawing on qualitative interviews with a group of 29 men who speak about their reported experiences and understandings of being fathered or growing up without biological fathers. Two major and intertwined subjugated discourses about adult men’s experiences of being fathered that counter- balance the prevailing discourses about meaning of fatherhood and fatherlessness became evident, namely, ‘being always there’ and ‘talking fatherhood’. The importance of the experience of fatherhood as ‘being there’, which relates to a quality of time and relationship between child and father rather than physical time together, is illustrated. It is not only biological fathers who can ‘be there’ for their sons but also social fathers, other significant male role models and father figures who step in at different times in participants’ lives when biological fathers are unavailable for whatever reason. Second, many positive experiences of fathers or father figures that resist a traditional role of authority and control and subscribe to more nurturant and non-violent forms of care, represented as ‘talking’ fathers, are underlined. If we are to better understand the impact of colonial and apartheid history and its legacy on family life in contemporary society, there is a need for more historically and contextually informed studies on the meaning of fatherhood and fatherlessness.Web of Scienc

Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum

A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any desired order. This leads to an efficient procedure to compute quantum reaction rates and the associated Gamov-Siegert resonances. In the classical limit the QNF reduces to the classical normal form which leads to the recently developed phase space realisation of Wigner's transition state theory. It is shown that the phase space structures that govern the classical reaction d ynamicsform a skeleton for the quantum scattering and resonance wavefunctions which can also be computed from the QNF. Several examples are worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008) R1-R11

An assessment of functioning and non-functioning distractors in multiple-choice questions: a descriptive analysis

<p>Abstract</p> <p>Background</p> <p>Four- or five-option multiple choice questions (MCQs) are the standard in health-science disciplines, both on certification-level examinations and on in-house developed tests. Previous research has shown, however, that few MCQs have three or four functioning distractors. The purpose of this study was to investigate non-functioning distractors in teacher-developed tests in one nursing program in an English-language university in Hong Kong.</p> <p>Methods</p> <p>Using item-analysis data, we assessed the proportion of non-functioning distractors on a sample of seven test papers administered to undergraduate nursing students. A total of 514 items were reviewed, including 2056 options (1542 distractors and 514 correct responses). Non-functioning options were defined as ones that were chosen by fewer than 5% of examinees and those with a positive option discrimination statistic.</p> <p>Results</p> <p>The proportion of items containing 0, 1, 2, and 3 functioning distractors was 12.3%, 34.8%, 39.1%, and 13.8% respectively. Overall, items contained an average of 1.54 (SD = 0.88) functioning distractors. Only 52.2% (n = 805) of all distractors were functioning effectively and 10.2% (n = 158) had a choice frequency of 0. Items with more functioning distractors were more difficult and more discriminating.</p> <p>Conclusion</p> <p>The low frequency of items with three functioning distractors in the four-option items in this study suggests that teachers have difficulty developing plausible distractors for most MCQs. Test items should consist of as many options as is feasible given the item content and the number of plausible distractors; in most cases this would be three. Item analysis results can be used to identify and remove non-functioning distractors from MCQs that have been used in previous tests.</p