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 'factorizing' 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 factorized. The conditions under which this is possible are examined. Examples are presented.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Australian Newspaper History Group Newsletter

Current findings related to the history of Australian newspapers.

Australian Newspaper History Group Newsletter

Current findings, news and announcements related to the history of Australian newspapers.

Australian Newspaper History Group Newsletter

Current findings, news and announcements related to the history of Australian newspapers.

Group outside the Sub Inspector Office during Ky visit

Group of people outside the Sub Inspector Office during visit of former South Vietnamese vice president Nguyen Cao Ky to Brisbane, Australia in January 1967.

Group of marchers during Mayday procession 1966 Brisbane, Australia

Group of marchers during Mayday procession 1966 Brisbane, Australia including children and dog. The group is passing Pearl Assurance House in Queen Street, Brisbane. Marchers have flags and banners relating to anti war and anti nuclear tests.

Quantum dynamics of three coupled atomic Bose-Einstein condensates

The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.

Traditional architecture in the Pacific

Architecture of the Pacific covers a region of more than third of the earth’s surface. The sparse Pacific population spreads over some 30 000 islands, which graduate in size from small atolls to the largest island, Australia, a continent. Pacific architecture can be studied as four cultural units: Micronesia, Polynesia, Melanesia, and Australasia (Australia and New Zealand). While many of the islands of Micronesia lie above the Equator, the remaining Pacific islands are in the southern hemisphere. With the exception of Australia, most of the islands have a warm and humid tropical climate with high rainfalls and lush vegetation. Some islands lie in the cyclonic and earthquake belts. Two distinct racial groups settled the region. The indigenous people, the Micronesians, Melanesians, Polynesians, Australian Aborigines and New Zealand Maoris, migrated from Asia thousands of years ago. The second group, the recent immigrants, were Europeans, who occupied the region during the last two centuries, and pockets of Asians brought in by colonial administrations as labourers during the early twentieth century.

Undergraduate student experiences and perceptions of group projects

This paper reports the experiences and perceptions of student group projects of three cohorts of undergraduates: a 3rd year capstone course in professional communication (N = 54), a 3rd year elective in chemical engineering (N = 29), and a core 2nd-year course in chemical engineering (N = 74).

Megan Henderson and Gay Walkington in Wattle Dance Group, Christmas 1968

Megan Henderson and Gay Walkington in Wattle Dance Group, Christmas 1968. The Wattle Dance Group met every Saturday in the Trades Hall, Brisbane, Australia. They held an concert at the end of each year. Janet Henderson was the mainstay and taught along with a few others. Jean Leary was the pianist. She took over from Eva Bacon.

June Hill in Wattle Dance Group, Christmas 1968

June Hill in Wattle Dance Group, Christmas 1968. The Wattle Dance Group met every Saturday in the Trades Hall, Brisbane, Australia. They held an concert at the end of each year. Janet Henderson was the mainstay and taught along with a few others. Jean Leary was the pianist. She took over from Eva Bacon.

Julie Walkington and Karlin Bracegirdle in Wattle Dance Group, Christmas 1968

Julie Walkington and Karlin Bracegirdle in Wattle Dance Group, Christmas 1968. The Wattle Dance Group met every Saturday in the Trades Hall, Brisbane, Australia. They held an concert at the end of each year. Janet Henderson was the mainstay and taught along with a few others. Jean Leary was the pianist. She took over from Eva Bacon.

The Indotriradites dolianitii Morphon, a distinctive group of miospore species from the Lower Carboniferous of Gondwana

An emended diagnosis and generic reallocation are proposed for the trilete miospore Indotriradites dolianitii (Daemon, 1974) Loboziak et al., comb. nov. A new species, I. daemonii Loboziak et al., sp. nov., from Viséan strata of Western Gondwana, is erected. These two species, together with I. zosteriformis (Playford et Satterthwait) Playford, 1991 from the Viséan of Australia, belong to a cohesive morphological miospore category, here termed the Indotriradites dolianitii Morphon, which is evidently restricted to the Lower Carboniferous of Gondwana.

Prevention of child behavior problems through universal implementation of a group behavioral family intervention.

The aim of this mental health promotion initiative was to evaluate the effectiveness of a universally delivered group behavioral family intervention (BFI) in preventing behavior problems in children. This study investigates the transferability of an efficacious clinical program to a universal prevention intervention delivered through child and community health services targeting parents of preschoolers within a metropolitan health region. A quasiexperimental two-group (BFI, n=804 vs. Comparison group, n=806) longitudinal design followed preschool aged children and their parents over a 2-year period. BFI was associated with significant reductions in parent-reported levels of dysfunctional parenting and parent-reported levels of child behavior problems. Effect sizes on child behavior problems ranged from large (.83) to moderate (.47). Positive and significant effects were also observed in parent mental health, marital adjustment, and levels of child rearing conflict. Findings are discussed with respect to their implication for significant population reductions in child behavior problems as well as the pragmatic challenges for prevention science in encouraging both the evaluation and uptake of preventive initiatives in real world settings.