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.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

gl(2 vertical bar 2) current superalgebra and non-unitary conformal field theory

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2\2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented. (C) 2003 Elsevier B.V. All rights reserved.

Petrology and geochemistry of early cretaceous bimodal continental flood volcanism of the NW Etendeka, Namibia. Part 2: Characteristics and petrogenesis of the high-Ti latite and high-Ti and low-Ti voluminous quartz latite eruptives

As a result of their relative concentration towards the respective Atlantic margins, the silicic eruptives of the Parana (Brazil)-Etendeka large igneous province are disproportionately abundant in the Etendeka of Namibia. The NW Etendeka silicic units, dated at similar to132 Ma, occupy the upper stratigraphic levels of the volcanic sequences, restricted to the coastal zone, and comprise three latites and five quartz latites (QL). The large-volume Fria QL is the only low-Ti type. Its trace element and isotopic signatures indicate massive crustal input. The remaining NW Etendeka silicic units are enigmatic high-Ti types, geochemically different from low-Ti types. They exhibit chemical affinities with the temporally overlapping Khumib high-Ti basalt (see Ewart et al. Part 1) and high crystallization temperatures (greater than or equal to980 to 1120degreesC) inferred from augite and pigeonite phenocrysts, both consistent with their evolution from a mafic source. Geochemically, the high-Ti units define three groups, thought genetically related. We test whether these represent independent liquid lines of descent from a common high-Ti mafic parent. Although the recognition of latites reduces the apparent silica gap, difficulty is encountered in fractional crystallization models by the large volumes of two QL units. Numerical modelling does, however, support large-scale open-system fractional crystallization, assimilation of silicic to basaltic materials, and magma mixing, but cannot entirely exclude partial melting processes within the temporally active extensional environment. The fractional crystallization and mixing signatures add to the complexity of these enigmatic and controversial silicic magmas. The existence, however, of temporally and spatially overlapping high-Ti basalts is, in our view, not coincidental and the high-Ti character of the silicic magmas ultimately reflects a mantle signature.

An evaluation of the time dependence of the anisotropy of the water diffusion tensor in acute human ischemia

We have performed MRI examinations to determine the water diffusion tensor in the brain of six patients who were admitted to the hospital within 12 h after the onset of cerebral ischemic symptoms. The examinations have been carried out immediately after admission, and thereafter at varying intervals up to 90 days post admission. Maps of the trace of the diffusion tensor, the fractional anisotropy and the lattice index, as well as maps of cerebral blood perfusion parameters, were generated to quantitatively assess the character of the water diffusion tensor in the infarcted area. In patients with significant perfusion deficits and substantial lesion volume changes, four of six cases, our measurements show a monotonic and significant decrease in the diffusion anisotropy within the ischemic lesion as a function of time. We propose that retrospective analysis of this quantity, in combination with brain tissue segmentation and cerebral perfusion maps, may be used in future studies to assess the severity of the ischemic event. (C) 1999 Elsevier Science Inc.

On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

Discrete teleportation protocol of continuum spectra field states

A discrete protocol for teleportation of superpositions of coherent states of optical-cavity fields is presented. Displacement and parity operators are unconventionally used in Bell-like measurement for field states.

Effects of harvesting callianassid (ghost) shrimps on subtropical benthic communities

The effects of harvesting of callianassid shrimp (Trypaea australiensis) on the abundance and composition of macrobenthic assemblages in unvegetated sediments of a subtropical coastal embayment in Queensland, Australia were examined using a combination of sampling and manipulative experiments. First, the abundance and composition of the benthic infauna in an area regularly used for the collection of shrimp for bait by recreational anglers was compared with multiple reference areas. Second, a BACI design, with multiple reference areas, was used to examine the short-term effects of harvesting on the benthic assemblages from an intensive commercialised fishing competition. Third, a large-scale, controlled manipulative experiment, where shrimp were harvested from 10,000 m(2) plots at intensities commensurate with those from recreational and commercial operators, was done to determine the impacts on different components of the infaunal assemblage. Only a few benthic taxa showed significant declines in abundance in response to the removal of ghost shrimp from the unvegetated sediments. There was evidence, however, of more subtle effects with changes in the degree of spatial variation (patchiness) of several taxa as a result of harvesting.. Groups such as capitellid polychaetes, gammarid amphipods and some bivalves were significantly more patchy in their distribution in areas subjected to harvesting than reference areas, at a scale of tens of metres. This scale corresponds to the patterns of movement and activity of recreational harvesters working in these areas. In contrast, patchiness in the abundance of ghost shrimp decreased significantly under harvesting at scales of hundreds of metres, in response to harvesters focussing their efforts on areas with greater numbers of burrow entrances, leading to a more even distribution of the animals. Controlled experimental harvesting caused declines in the abundance of soldier crabs (Mictyris longicarpus), polychaetes and amphipods and an increase in the spatial patchiness of polychaetes. Populations of ghost shrimp were, however, resilient to harvesting over extended periods of time. In conclusion, harvesting of ghost shrimp for bait by recreational and commercial fishers causes significant but localised impacts on a limited range of benthic fauna in unvegetated sediments, including changes in the degree of spatial patchiness in their distribution. (c) 2005 Elsevier B.V. All rights reserved.

Programs as paths: An approach to timing constraint analysis

A program can be decomposed into a set of possible execution paths. These can be described in terms of primitives such as assignments, assumptions and coercions, and composition operators such as sequential composition and nondeterministic choice as well as finitely or infinitely iterated sequential composition. Some of these paths cannot possibly be followed (they are dead or infeasible), and they may or may not terminate. Decomposing programs into paths provides a foundation for analyzing properties of programs. Our motivation is timing constraint analysis of real-time programs, but the same techniques can be applied in other areas such as program testing. In general the set of execution paths for a program is infinite. For timing analysis we would like to decompose a program into a finite set of subpaths that covers all possible execution paths, in the sense that we only have to analyze the subpaths in order to determine suitable timing constraints that cover all execution paths.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].