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

Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics

The problem of studying the quantum Hall effect on manifolds with nonconstant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The hyperbolic disk is also considered and some other applications of this approach are discussed as well.Comment: 16 page

Trauma as counter-revolutionary colonisation: narratives from (post)revolutionary Egypt

We argue that multiple levels of trauma were present in Egypt before, during and after the 2011 revolution. Individual, social and political trauma constitute a triangle of traumatisation which was strategically employed by the Egyptian counter-revolutionary forces – primarily the army and the leadership of the Muslim Brotherhood – to maintain their political and economic power over and above the social, economic and political interests of others. Through the destruction of physical bodies, the fragmentation and polarisation of social relations and the violent closure of the newly emerged political public sphere, these actors actively repressed the potential for creative and revolutionary transformation. To better understand this multi-layered notion of trauma, we turn to Habermas’ ‘colonisation of the lifeworld’ thesis which offers a critical lens through which to examine the wider political and economic structures and context in which trauma occurred as well as its effects on the personal, social and political realms. In doing so, we develop a novel conception of trauma that acknowledges individual, social and political dimensions. We apply this conceptual framing to empirical narratives of trauma in Egypt’s pre- and post-revolutionary phases, thus both developing a non-Western application of Habermas’ framework and revealing ethnographic accounts of the revolution by activists in Cairo

On boson algebras as Hopf algebras

Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding $R$-matrices. It is also shown that a class of generalized Heisenberg algebras including those algebras including those underlying physical models such as that of Calogero-Sutherland, is isomorphic with one of the types of boson algebra proposed, and can be formulated as a Hopf algebra.Comment: LaTex, 18 page

Reproductive and developmental effects of disinfection by-products in drinking water.

Recent epidemiologic studies have reported associations between the consumption of chlorinated drinking water and reproductive and developmental effects. Here we review the available epidemiologic data, assess the hazard potential posed by exposure to disinfection by-products, identify critical data gaps, and offer recommendations for further research. The epidemiologic evidence supporting associations between exposure to water disinfection by-products (DBPs) and adverse pregnancy outcomes is sparse, and positive findings should be interpreted cautiously. The methods used during the early stages of research in this area have been diverse. Variability in exposure assessment and endpoints makes it difficult to synthesize or combine the available data. Exposure misclassification and unmeasured confounding may have lead to bias in risk estimation. Future studies of reproductive outcome and exposure to chlorinated water should use improved methods for exposure assessment to 1) assure selection of appropriate exposure markers, 2) assess seasonal and annual fluctuations in DBPs, 3) assess variability within the distribution system, and 4) assess exposure through multiple routes such as bathing and showering, as well as consumption. Population-based studies should be conducted to evaluate male and female fertility, conception delay, growth retardation, and specific birth defects. The reproductive and developmental effects of exposure to DBPs could be efficiently explored in ongoing investigations by incorporating valid exposure markers and relevant questionnaire information. Future studies should make use of naturally occurring variability in the concentrations of DBPs and may incorporate biomarkers of exposure and effect in their design. Epidemiologic investigations should be conducted in parallel with laboratory-based and animal studies in a coordinated, multidisciplinary approach

Free Dirac evolution as a quantum random walk

Any positive-energy state of a free Dirac particle that is initially highly-localized, evolves in time by spreading at speeds close to the speed of light. This general phenomenon is explained by the fact that the Dirac evolution can be approximated arbitrarily closely by a quantum random walk, where the roles of coin and walker systems are naturally attributed to the spin and position degrees of freedom of the particle. Initially entangled and spatially localized spin-position states evolve with asymptotic two-horned distributions of the position probability, familiar from earlier studies of quantum walks. For the Dirac particle, the two horns travel apart at close to the speed of light.Comment: 16 pages, 1 figure. Latex2e fil

Socioecology Explains Individual Variation in Urban Space Use in Response to Management in Cape Chacma Baboons (Papio ursinus)

The presence of wildlife adjacent to and within urban spaces is a growing phenomenon globally. When wildlife’s presence in urban spaces has negative impacts for people and wildlife, nonlethal and lethal interventions on animals invariably result. Recent evidence suggests that individuals in wild animal populations vary in both their propensity to use urban space and their response to nonlethal management methods. Understanding such interindividual differences and the drivers of urban space use could help inform management strategies. We use direct observation and high-resolution GPS (1 Hz) to track the space use of 13 adult individuals in a group of chacma baboons (Papio ursinus) living at the urban edge in Cape Town, South Africa. The group is managed by a dedicated team of field rangers, who use aversive conditioning to reduce the time spent by the group in urban spaces. Adult males are larger, more assertive, and more inclined to enter houses, and as such are disproportionately subject to “last resort” lethal management. Field rangers therefore focus efforts on curbing the movements of adult males, which, together with high-ranking females and their offspring, comprise the bulk of the group. However, our results reveal that this focus allows low-ranking, socially peripheral female baboons greater access to urban spaces. We suggest that movement of these females into urban spaces, alone or in small groups, is an adaptive response to management interventions, especially given that they have no natural predators. These results highlight the importance of conducting behavioral studies in conjunction with wildlife management, to ensure effective mitigation techniques

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying Uq(sl(2|1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.Comment: 26 pages, no figures, LaTe

Finite dimensional representations of Uq(C(n+1))U_q(C(n+1)) at arbitrary qq

A method is developed to construct irreducible representations(irreps) of the quantum supergroup $U_q(C(n+1))$ in a systematic fashion. It is shown that every finite dimensional irrep of this quantum supergroup at generic $q$ is a deformation of a finite dimensional irrep of its underlying Lie superalgebra $C(n+1)$, and is essentially uniquely characterized by a highest weight. The character of the irrep is given. When $q$ is a root of unity, all irreps of $U_q(C(n+1))$ are finite dimensional; multiply atypical highest weight irreps and (semi)cyclic irreps also exist. As examples, all the highest weight and (semi)cyclic irreps of $U_q(C(2))$ are thoroughly studied.Comment: 21 page