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.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

A Poincare-Birkhoff-Witt commutator lemma for U-q[gl(m vertical bar n)]

We present and prove in detail a Poincare-Birkhoff-Witt commutator lemma for the quantum superalgebra U-q[gl(m\n)]. (C) 2003 American Institute of Physics.

Career development and systems theory: Connecting theory and practice

The Systems Theory Framework was developed to produce a metatheoretical framework through which the contribution of all theories to our understanding of career behaviour could be recognised. In addition it emphasises the individual as the site for the integration of theory and practice. Its utility has become more broadly acknowledged through its application to a range of cultural groups and settings, qualitative assessment processes, career counselling, and multicultural career counselling. For these reasons, the STF is a very valuable addition to the field of career theory. In viewing the field of career theory as a system, open to changes and developments from within itself and through constantly interrelating with other systems, the STF and this book is adding to the pattern of knowledge and relationships within the career field. The contents of this book will be integrated within the field as representative of a shift in understanding existing relationships within and between theories. In the same way, each reader will integrate the contents of the book within their existing views about the current state of career theory and within their current theory-practice relationship. This book should be required reading for anyone involved in career theory. It is also highly suitable as a text for an advanced career counselling or theory course.

Prejudiced attitudes, group norms, and discriminatory behaviour

Most current attitude research focuses on range of non-social attitudinal targets, including health-related and consumer outcomes. In this paper, a program of research that considers the relations among intergroup attitudes, group norms, and behavior will be described. The first study examined the effect of ingroup norms relating to multiculturalism on the extent to wich participants hehaviourally enacted their attitudes. Consistent with social identity theory, attitudebehaviour consistency in relation was influenced by ingroup norms, particularly when national identity was salient. The results of a large scale field study that essential replicated this pattern of results will also be discussed.

Employee group memberships and organisational communication during organisational change

The preset study adopted an intergroup approach to information sharing and communication in three organisational samples during change. In Study 1, employees from a public hospital (N = 142) completed a survey measuring perceptions of organisational communication and strength of identification with the work unit and the organisation as a whole. Consistent with predictions, team members rated communication from double ingroup members (same work unit/same occupational group) more favourably than communication from partial group members (same work unit/different occupational group). Also as predicted, work unit identification was related to favourable ratings of work unit communication across occupational groups, whereas occupational identification was related to favourable ratings of work unit communication within occupational groups. In Study 2, strength of identification with three organisational groups was associated with positive ratings of communication among employees from the same public hospital (N = 189) and a military organisation (N = 2119). Based on these results, intergroup strategies for the management of information sharing and organisational communication during change are discussed.

I'm a hypocrite, but so is everyone else: Group support and the reduction of cognitive dissonance

The impact of social support on dissonance arousal was investigated from a social identity view of dissonance theory. This perspective is seen as augmenting current conceptualizations of dissonance theory by predicting when normative information will impact on dissonance arousal and by indicating the availability of identity-related strategies of dissonance reduction. An experiment was conducted to induce feelings of hypocrisy under conditions of behavioral support or nonsupport. Group salience was either high or low, or individual identity was emphasized. As predicted, participants with no support from the salient in-group exhibited the greatest need to reduce dissonance through attitude change and reduced levels of group identification. Results were interpreted in terms of self being central to the arousal and reduction of dissonance.

Responses to a merger: The effects of premerger group status and integration pattern

Adopting a social identity perspective, the research was designed to examine the interplay between premerger group status and integration pattern in the prediction of responses to a merger. The research employed a 2 (status: high versus low) x 3 (integration pattern: assimilation versus integrational equality versus transformation) between-participants factorial design. We predicted that integration pattern and group status would interact such that the responses of the members of high status group would be most positive under conditions of an assimilation pattern, whereas members of low status groups were expected to favour an integration-equality pattern. After working on a task in small groups, group status was manipulated and the groups worked on a second task. The merger was then announced and the integration pattern was manipulated (e.g., in terms of the logo, location, and decision rules). The main dependent variables were assessed after the merged groups had worked together on a third task. As expected, there was evidence that the effects of group status on responses to the merger were moderated by integration pattern. Field data also indicated that both premerger status and perceived integration pattern influenced employee responses to an organisational merger.

Ex ante evaluations of alternate data structures for end user queries: Theory and experimental test

The data structure of an information system can significantly impact the ability of end users to efficiently and effectively retrieve the information they need. This research develops a methodology for evaluating, ex ante, the relative desirability of alternative data structures for end user queries. This research theorizes that the data structure that yields the lowest weighted average complexity for a representative sample of information requests is the most desirable data structure for end user queries. The theory was tested in an experiment that compared queries from two different relational database schemas. As theorized, end users querying the data structure associated with the less complex queries performed better Complexity was measured using three different Halstead metrics. Each of the three metrics provided excellent predictions of end user performance. This research supplies strong evidence that organizations can use complexity metrics to evaluate, ex ante, the desirability of alternate data structures. Organizations can use these evaluations to enhance the efficient and effective retrieval of information by creating data structures that minimize end user query complexity.

Impact of social group processes and functional diversity on communication in networked organizations

This study examines the role of social group processes in perceptions of effective communication in Australian Cooperative Research Centres (CRCs). Communication professionals in 25 CRCs discussed the barriers and opportunities for communication in their diverse networked organizations. Thematic analysis of the transcripts highlighted the contribution of social group processes to both barriers and opportunities. Communication challenges implicated the social identity of organizational members, many of which were associated with distinct structural aspects of these organizations. Opportunities for communication frequently involved features that implicated social identity, including taking advantage of existing organizational or industry identities, preventing conflicting identities from becoming salient, and promoting a collective CRC identity.

Selecting optimal instantiations of data models - Theory and validation of an ex ante approach

The schema of an information system can significantly impact the ability of end users to efficiently and effectively retrieve the information they need. Obtaining quickly the appropriate data increases the likelihood that an organization will make good decisions and respond adeptly to challenges. This research presents and validates a methodology for evaluating, ex ante, the relative desirability of alternative instantiations of a model of data. In contrast to prior research, each instantiation is based on a different formal theory. This research theorizes that the instantiation that yields the lowest weighted average query complexity for a representative sample of information requests is the most desirable instantiation for end-user queries. The theory was validated by an experiment that compared end-user performance using an instantiation of a data structure based on the relational model of data with performance using the corresponding instantiation of the data structure based on the object-relational model of data. Complexity was measured using three different Halstead metrics: program length, difficulty, and effort. For a representative sample of queries, the average complexity using each instantiation was calculated. As theorized, end users querying the instantiation with the lower average complexity made fewer semantic errors, i.e., were more effective at composing queries. (c) 2005 Elsevier B.V. All rights reserved.