Non-positivity of Groenewold operators

A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Liouville densities, leading to what may be termed term Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Liouville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.Comment: 9 pages, 1 figures, submitted to Europhysics Letter

The quantum state vector in phase space and Gabor's windowed Fourier transform

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed `window state vector'. Here aspects of this construction are explored, with emphasis on the connection with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of window are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schr\"odinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and further references adde

Phase space spinor amplitudes for spin 1/2 systems

The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-\half is treated in detail, and it is shown that phase space amplitudes on the sphere transform correctly as spinors under under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-\half magnetic dipole in a time-dependent magnetic field.Comment: 19 pages, added new results, fixed typo

Conservation laws for invariant functionals containing compositions

The study of problems of the calculus of variations with compositions is a quite recent subject with origin in dynamical systems governed by chaotic maps. Available results are reduced to a generalized Euler-Lagrange equation that contains a new term involving inverse images of the minimizing trajectories. In this work we prove a generalization of the necessary optimality condition of DuBois-Reymond for variational problems with compositions. With the help of the new obtained condition, a Noether-type theorem is proved. An application of our main result is given to a problem appearing in the chaotic setting when one consider maps that are ergodic.Comment: Accepted for an oral presentation at the 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), to be held in Pretoria, South Africa, 22-24 August, 200

Eigenvalus of Casimir Invariants for Type-I Quantum Superalgebras

We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.Comment: 13 pages, AmsTex file; to appear in Lett. Math. Phy

Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.Comment: 13 page

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 disks 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 Hilbert space carrying the positive discrete series representations of the algebra su(1,1)or so(2,1). The explicit relation between the spectra of operators associated with disks and circles with proportional radii, is given in terms of the dicrete variable Meixner polynomials.Comment: 11 pages, latex fil

Presence and television.

Film and a number of emerging entertainment technologies offer media consumers an illusion of nonmediation known as presence. To investigate the possibility that television can evoke presence, 65 undergraduate students were shown brief examples of rapid point-of-view movement from commercially available videotapes on a television with either a small screen (12 inches [30.5 cm], measured diagonally) or a large screen (46 inches [116.8 cm]). Participants\u27 responses were measured via a questionnaire and a computer-based recording of arousal (electrodermal activity). Viewers of both televisions reported an enjoyable sense of physical movement, excitement, involvement, and a sense of participation. Furthermore, as predicted, participants who watched the large screen television thought the movement in the scenes was faster, experienced a greater sense of physical movement, enjoyed the movement to a greater extent, found the viewing experience more exciting, and were more physiologically aroused. Practical and theoretical implications are discussed

A Chiral Schwinger model, its Constraint Structure and Applications to its Quantization

The Jackiw-Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac brackets. By introducing an additional scalar field, it is shown that the model can be made gauge invariant. The gauge invariant model is quantized by establishing a pair of gauge fixing constraints in order that the method of Dirac can be used.Comment: 18 page

ADRIC: Adverse Drug Reactions In Children - a programme of research using mixed methods

Aims To comprehensively investigate the incidence, nature and risk factors of adverse drug reactions (ADRs) in a hospital-based population of children, with rigorous assessment of causality, severity and avoidability, and to assess the consequent impact on children and families. We aimed to improve the assessment of ADRs by development of new tools to assess causality and avoidability, and to minimise the impact on families by developing better strategies for communication. Review methods Two prospective observational studies, each over 1 year, were conducted to assess ADRs in children associated with admission to hospital, and those occurring in children who were in hospital for longer than 48 hours. We conducted a comprehensive systematic review of ADRs in children. We used the findings from these studies to develop and validate tools to assess causality and avoidability of ADRs, and conducted interviews with parents and children who had experienced ADRs, using these findings to develop a leaflet for parents to inform a communication strategy about ADRs. Results The estimated incidence of ADRs detected in children on admission to hospital was 2.9% [95% confidence interval (CI) 2.5% to 3.3%]. Of the reactions, 22.1% (95% CI 17% to 28%) were either definitely or possibly avoidable. Prescriptions originating in the community accounted for 44 out of 249 (17.7%) of ADRs, the remainder originating from hospital. A total of 120 out of 249 (48.2%) reactions resulted from treatment for malignancies. Off-label and/or unlicensed (OLUL) medicines were more likely to be implicated in an ADR than authorised medicines [relative risk (RR) 1.67, 95% CI 1.38 to 2.02; p  48 hours, the overall incidence of definite and probable ADRs based on all admissions was 15.9% (95% CI 15.0 to 16.8). Opiate analgesic drugs and drugs used in general anaesthesia (GA) accounted for > 50% of all drugs implicated in ADRs. The odds ratio of an OLUL drug being implicated in an ADR compared with an authorised drug was 2.25 (95% CI 1.95 to 2.59; p < 0.001). Risk factors identified were exposure to a GA, age, oncology treatment and number of medicines. The systematic review estimated that the incidence rates for ADRs causing hospital admission ranged from 0.4% to 10.3% of all children [pooled estimate of 2.9% (95% CI 2.6% to 3.1%)] and from 0.6% to 16.8% of all children exposed to a drug during hospital stay. New tools to assess causality and avoidability of ADRs have been developed and validated. Many parents described being dissatisfied with clinician communication about ADRs, whereas parents of children with cancer emphasised confidence in clinician management of ADRs and the way clinicians communicated about medicines. The accounts of children and young people largely reflected parents’ accounts. Clinicians described using all of the features of communication that parents wanted to see, but made active decisions about when and what to communicate to families about suspected ADRs, which meant that communication may not always match families’ needs and expectations. We developed a leaflet to assist clinicians in communicating ADRs to parents. Conclusion The Adverse Drug Reactions In Children (ADRIC) programme has provided the most comprehensive assessment, to date, of the size and nature of ADRs in children presenting to, and cared for in, hospital, and the outputs that have resulted will improve the management and understanding of ADRs in children and adults within the NHS. Recommendations for future research: assess the values that parents and children place on the use of different medicines and the risks that they will find acceptable within these contexts; focusing on high-risk drugs identified in ADRIC, determine the optimum drug dose for children through the development of a gold standard practice for the extrapolation of adult drug doses, alongside targeted pharmacokinetic/pharmacodynamic studies; assess the research and clinical applications of the Liverpool Causality Assessment Tool and the Liverpool Avoidability Assessment Tool; evaluate, in more detail, morbidities associated with anaesthesia and surgery in children, including follow-up in the community and in the home setting and an assessment of the most appropriate treatment regimens to prevent pain, vomiting and other postoperative complications; further evaluate strategies for communication with families, children and young people about ADRs; and quantify ADRs in other settings, for example critical care and neonatology