Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips $S$-matrix is unitarily related to the $S$-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\sigma$ of the Lax-Phillips theory. Analytic continuation in $\sigma$ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision

Flow Dynamics And Plasma Heating Of Spheromaks In SSX

We report several new experimental results related to flow dynamics and heating from single dipole-trapped spheromaks and spheromak merging studies at SSX. Single spheromaks (stabilized with a pair of external coils, see Brown, Phys. Plasmas 13 102503 (2006)) and merged FRC-like configurations (see Brown, Phys. Plasmas 13, 056503 (2006)) are trapped in our prolate (R = 0.2 m, L = 0.6 m) copper flux conserver. Local spheromak flow is studied with two Mach probes (r(1) = rho(i) ) calibrated by time-of-flight with a fast set of magnetic probes at the edge of the device. Both Mach probes feature six ion collectors housed in a boron nitride sheath. The larger Mach probe will ultimately be used in the MST reversed field pinch. Line averaged flow is measured by ion Doppler spectroscopy (IDS) at the midplane. The SSX IDS instrument measures with 1 mu s or better time resolution the width and Doppler shift of the C-III impurity (H plasma) 229.7 nm line to determine the temperature and line-averaged flow velocity (see Cothran, RSI 77, 063504 (2006)). We find axial flows up to 100 km/s during formation of the dipole trapped spheromak. Flow returns at the wall to form a large vortex. Recent high-resolution IDS velocity measurements during spheromak merging show bi-directional outflow jets at +/- 40 km/s (nearly the Alfven speed). We also measure T-i \u3e= 80 eV and T-e \u3e= 20 eV during spheromak merging events after all plasma facing surfaces are cleaned with helium glow discharge conditioning. Transient electron heating is inferred from bursts on a four-channel soft x-ray array. The spheromaks are also characterized by a suite of magnetic probe arrays for magnetic structure B(r,t), and interferometry for n(e) . Finally, we are designing a new oblate, trapezoidal flux conserver for FRC studies. Equilibrium and dynamical simulations suggest that a tilt-stable, oblate FRC can be formed by spheromak merging in the new flux conserver

Mechanotransduction and hyperpolarization-activated currents contribute to spontaneous activity in mouse vestibular ganglion neurons

The hyperpolarization-activated, cyclic nucleotide–sensitive current, Ih, is present in vestibular hair cells and vestibular ganglion neurons, and is required for normal balance function. We sought to identify the molecular correlates and functional relevance of Ih in vestibular ganglion neurons. Ih is carried by channels consisting of homo- or heteromeric assemblies of four protein subunits from the Hcn gene family. The relative expression of Hcn1–4 mRNA was examined using a quantitative reverse transcription PCR (RT-PCR) screen. Hcn2 was the most highly expressed subunit in vestibular neuron cell bodies. Immunolocalization of HCN2 revealed robust expression in cell bodies of all vestibular ganglion neurons. To characterize Ih in vestibular neuron cell bodies and at hair cell–afferent synapses, we developed an intact, ex vivo preparation. We found robust physiological expression of Ih in 89% of cell bodies and 100% of calyx terminals. Ih was significantly larger in calyx terminals than in cell bodies; however, other biophysical characteristics were similar. Ih was absent in calyces lacking Hcn1 and Hcn2, but small Ih was still present in cell bodies, which suggests expression of an additional subunit, perhaps Hcn4. To determine the contributions of hair cell mechanotransduction and Ih to the firing patterns of calyx terminals, we recorded action potentials in current-clamp mode. Mechanotransduction currents were modulated by hair bundle defection and application of calcium chelators to disrupt tip links. Ih activity was modulated using ZD7288 and cAMP. We found that both hair cell transduction and Ih contribute to the rate and regularity of spontaneous action potentials in the vestibular afferent neurons. We propose that modulation of Ih in vestibular ganglion neurons may provide a mechanism for modulation of spontaneous activity in the vestibular periphery

Schwinger Algebra for Quaternionic Quantum Mechanics

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \to \infty$.Comment: 20 pages, Plain Te

Test offering, not additional information, may increase HIV testing uptake in a knowledgeable population

A CAJM journal article.Objectives: To evaluate patient HIV knowledge and testing experience and assess the effect of an HIV informational handout on HIV testing propensity. Design: Cross sectional, descriptive techniques were employed to assess demographics, HIV knowledge and HIV testing experience. A randomized controlled trial was performed to determine if an HIV/AIDS information sheet influenced testing propensity. Setting: Blantyre Adventist Hospital Outpatient Clinic. Subjects: Non-emergency patients over 18 years old attending during consulting hours. Interventions: All subjects answered a questionnaire. For the randomized controlled trial component, half received an HIV information handout. Main Outcome Measures: Proportions were calculated to evaluate testing experience. Logistic regression was used to assess impact of written information and demographics on HIV testing propensity. Results: 490 participants were recruited, of whom 57% had never been tested for HIV. Of the untested, 88% had never been offered an HIV test. Of those that had never been offered a test, 46% desired one. The sample was highly knowledgeable about HIV. Reading an information sheet had no impact on HIV knowledge (p=0.736 to 0.788) or desire for testing (p=0.387). However, age (OR=0.97,95%CI (0.95,0.99)) and gender (OR=1.85, 95%CI (1.06, 3.23)) significantly correlated with testing propensity. Conclusions: A large percentage of patients who have never been offered HIV testing desire testing. More frequent HIV test offering by clinicians could improve testing rates. Clinician education programmes should be developed to increase test offering. Furthermore, written health information in a setting of high HIV/AIDS knowledge may not change behaviour. Alternative methods should be employed to encourage HIV testing uptake

Infants' goal anticipation during failed and successful reaching actions

The ability to interpret and predict the actions of others is crucial to social interaction and to social, cognitive, and linguistic development. The current study provided a strong test of this predictive ability by assessing (1) whether infants are capable of prospectively processing actions that fail to achieve their intended outcome, and (2) how infants respond to events in which their initial predictions are not confirmed. Using eye tracking, 8‐month‐olds, 10‐month‐olds, and adults watched an actor repeatedly reach over a barrier to either successfully or unsuccessfully retrieve a ball. Ten‐month‐olds and adults produced anticipatory looks to the ball, even when the action was unsuccessful and the actor never achieved his goal. Moreover, they revised their initial predictions in response to accumulating evidence of the actor's failure. Eight‐month‐olds showed anticipatory looking only after seeing the actor successfully grasp and retrieve the ball. Results support a flexible, prospective social information processing ability that emerges during the first year of life. The ability to make predictions about the actions of others is crucial to social interaction and to social, cognitive, and linguistic development. The current study examined this ability in infancy by assessing (1) whether infants can prospectively process actions that fail to achieve their intended outcome, and (2) how infants respond to events in which their initial predictions are not confirmed. Using eye tracking, 8‐month‐olds, 10‐month‐olds, and adults watched an actor repeatedly reach over a barrier to successfully or unsuccessfully retrieve a ball. Results provide support for a flexible, prospective social information processing ability that emerges during the first year.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102162/1/desc12095.pd

A New Relativistic High Temperature Bose-Einstein Condensation

We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by $\mu \leq m\leq 2M/\mu _K,$ where $\mu$ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space-time, and $\mu _K$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with nonzero chemical potential $\mu ,$ the mass spectrum is shown to be bounded by $|\mu |\leq m\leq 2M/\mu _K,$ and a special type of high-temperature Bose-Einstein condensation can occur. We study this Bose-Einstein condensation, and show that it corresponds to a phase transition from the sector of continuous relativistic mass distributions to a sector in which the boson mass distribution becomes sharp at a definite mass $M/\mu _K.$ This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.Comment: Latex, 22 page