Inference of hot star density stream properties from data on rotationally recurrent DACs

The information content of data on rotationally periodic recurrent discrete absorption components (DACs) in hot star wind emission lines is discussed. The data comprise optical depths tau(w,phi) as a function of dimensionless Doppler velocity w=(Deltalambda/lambda(0))(c/v(infinity)) and of time expressed in terms of stellar rotation angle phi. This is used to study the spatial distributions of density, radial and rotational velocities, and ionisation structures of the corotating wind streams to which recurrent DACs are conventionally attributed. The simplifying assumptions made to reduce the degrees of freedom in such structure distribution functions to match those in the DAC data are discussed and the problem then posed in terms of a bivariate relationship between tau(w, phi) and the radial velocity v(r)(r), transverse rotation rate Omega(r) and density rho(r, phi) structures of the streams. The discussion applies to cases where: the streams are equatorial; the system is seen edge on; the ionisation structure is approximated as uniform; the radial and transverse velocities are taken to be functions only of radial distance but the stream density is allowed to vary with azimuth. The last kinematic assumption essentially ignores the dynamical feedback of density on velocity and the relationship of this to fully dynamical models is discussed. The case of narrow streams is first considered, noting the result of Hamann et al. (2001) that the apparent acceleration of a narrow stream DAC is higher than the acceleration of the matter itself, so that the apparent slow acceleration of DACs cannot be attributed to the slowness of stellar rotation. Thus DACs either involve matter which accelerates slower than the general wind flow, or they are formed by structures which are not advected with the matter flow but propagate upstream (such as Abbott waves). It is then shown how, in the kinematic model approximation, the radial speed of the absorbing matter can be found by inversion of the apparent acceleration of the narrow DAC, for a given rotation law. The case of broad streams is more complex but also more informative. The observed tau(w,phi) is governed not only by v(r)(r) and Omega(r) of the absorbing stream matter but also by the density profile across the stream, determined by the azimuthal (phi(0)) distribution function F-0(phi(0)) of mass loss rate around the stellar equator. When F-0(phi(0)) is fairly wide in phi(0), the acceleration of the DAC peak tau(w, phi) in w is generally slow compared with that of a narrow stream DAC and the information on v(r)(r), Omega(r) and F- 0(phi(0)) is convoluted in the data tau(w, phi). We show that it is possible, in this kinematic model, to recover by inversion, complete information on all three distribution functions v(r)(r), Omega(r) and F-0(phi(0)) from data on tau(w, phi) of sufficiently high precision and resolution since v(r)(r) and Omega(r) occur in combination rather than independently in the equations. This is demonstrated for simulated data, including noise effects, and is discussed in relation to real data and to fully hydrodynamic models

The general harmonic-oscillator brackets: compact expression, symmetries, sums and Fortran code

We present a very simple expression and a Fortran code for the fast and precise calculation of three-dimensional harmonic-oscillator transformation brackets. The complete system of symmetries for the brackets along with analytical expressions for sums, containing products of two and three brackets, is given.Comment: 13 pages, accepted for publication in Nuclear Physics

Nuclear Spin Relaxation for Higher Spin

We study the relaxation of a spin I that is weakly coupled to a quantum mechanical environment. Starting from the microscopic description, we derive a system of coupled relaxation equations within the adiabatic approximation. These are valid for arbitrary I and also for a general stationary non--equilibrium state of the environment. In the case of equilibrium, the stationary solution of the equations becomes the correct Boltzmannian equilibrium distribution for given spin I. The relaxation towards the stationary solution is characterized by a set of relaxation times, the longest of which can be shorter, by a factor of up to 2I, than the relaxation time in the corresponding Bloch equations calculated in the standard perturbative way.Comment: 4 pages, Latex, 2 figure

Skyrmion Dynamics and NMR Line Shapes in QHE Ferromagnets

The low energy charged excitations in quantum Hall ferromagnets are topological defects in the spin orientation known as skyrmions. Recent experimental studies on nuclear magnetic resonance spectral line shapes in quantum well heterostructures show a transition from a motionally narrowed to a broader `frozen' line shape as the temperature is lowered at fixed filling factor. We present a skyrmion diffusion model that describes the experimental observations qualitatively and shows a time scale of $\sim 50 \mu{\rm sec}$ for the transport relaxation time of the skyrmions. The transition is characterized by an intermediate time regime that we demonstrate is weakly sensitive to the dynamics of the charged spin texture excitations and the sub-band electronic wave functions within our model. We also show that the spectral line shape is very sensitive to the nuclear polarization profile along the z-axis obtained through the optical pumping technique.Comment: 6 pages, 4 figure

The Grover algorithm with large nuclear spins in semiconductors

We show a possible way to implement the Grover algorithm in large nuclear spins 1/2<I<9/2 in semiconductors. The Grover sequence is performed by means of multiphoton transitions that distribute the spin amplitude between the nuclear spin states. They are distinguishable due to the quadrupolar splitting, which makes the nuclear spin levels non-equidistant. We introduce a generalized rotating frame for an effective Hamiltonian that governs the non-perturbative time evolution of the nuclear spin states for arbitrary spin lengths I. The larger the quadrupolar splitting, the better the agreement between our approximative method using the generalized rotating frame and exact numerical calculations.Comment: 11 pages, 18 EPS figures, REVTe

Skyrmions in the Fractional Quantum Hall Effect

It is verified that, at small Zeeman energies, the charged excitations in the vicinity of 1/3 filled Landau level are skyrmions of composite fermions, analogous to the skyrmions of electrons near filling factor unity. These are found to be relevant, however, only at very low magnetic fields.Comment: 13 pages including 2 postscript figures; accepted for publication in Solid State Communications (1996

Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions

A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the $\nu=1/3$, 2/5, and 3/7 gapped fractions, and find approximate agreement with numerical results. I also analyse the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 2/5 and 3/7, and it is shown that the spin-polarized 2/5 state, in contrast to the spin-polarized 1/3 state, cannot be described as a simple quantum ferromagnet.Comment: 18 pages, 18 encapsulated ps figure

Correlations of structural, magnetic, and dielectric properties of undoped and doped CaCu3Ti4O12

The present work reports synthesis, as well as a detailed and careful characterization of structural, magnetic, and dielectric properties of differently tempered undoped and doped CaCu3Ti4O12 (CCTO) ceramics. For this purpose, neutron and x-ray powder diffraction, SQUID measurements, and dielectric spectroscopy have been performed. Mn-, Fe-, and Ni-doped CCTO ceramics were investigated in great detail to document the influence of low-level doping with 3d metals on the antiferromagnetic structure and dielectric properties. In the light of possible magnetoelectric coupling in these doped ceramics, the dielectric measurements were also carried out in external magnetic fields up to 7 T, showing a minor but significant dependence of the dielectric constant on the applied magnetic field. Undoped CCTO is well-known for its colossal dielectric constant in a broad frequency and temperature range. With the present extended characterization of doped as well as undoped CCTO, we want to address the question why doping with only 1% Mn or 0.5% Fe decreases the room-temperature dielectric constant of CCTO by a factor of ~100 with a concomitant reduction of the conductivity, whereas 0.5% Ni doping changes the dielectric properties only slightly. In addition, diffraction experiments and magnetic investigations were undertaken to check for possible correlations of the magnitude of the colossal dielectric constants with structural details or with magnetic properties like the magnetic ordering, the Curie-Weiss temperatures, or the paramagnetic moment. It is revealed, that while the magnetic ordering temperature and the effective moment of all investigated CCTO ceramics are rather similar, there is a dramatic influence of doping and tempering time on the Curie-Weiss constant.Comment: 10 pages, 11 figure

NMR and NQR Fluctuation Effects in Layered Superconductors

We study the effect of thermal fluctuations of the s-wave order parameter of a quasi two dimensional superconductor on the nuclear spin relaxation rate near the transition temperature Tc. We consider both the effects of the amplitude fluctuations and the Berezinskii-Kosterlitz-Thouless (BKT) phase fluctuations in weakly coupled layered superconductors. In the treatment of the amplitude fluctuations we employ the Gaussian approximation and evaluate the longitudinal relaxation rate 1/T1 for a clean s-wave superconductor, with and without pair breaking effects, using the static pair fluctuation propagator D. The increase in 1/T1 due to pair breaking in D is overcompensated by the decrease arising from the single particle Green's functions. The result is a strong effect on 1/T1 for even a small amount of pair breaking. The phase fluctuations are described in terms of dynamical BKT excitations in the form of pancake vortex-antivortex (VA) pairs. We calculate the effect of the magnetic field fluctuations caused by the translational motion of VA excitations on 1/T1 and on the transverse relaxation rate 1/T2 on both sides of the BKT transitation temperature T(BKT)<Tc. The results for the NQR relaxation rates depend strongly on the diffusion constant that governs the motion of free and bound vortices as well as the annihilation of VA pairs. We discuss the relaxation rates for real multilayer systems where the diffusion constant can be small and thus increase the lifetime of a VA pair, leading to an enhancement of the rates. We also discuss in some detail the experimental feasibility of observing the effects of amplitude fluctuations in layered s-wave superconductors such as the dichalcogenides and the effects of phase fluctuations in s- or d-wave superconductors such as the layered cuprates.Comment: 38 pages, 12 figure

An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics

For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types