The hydrodynamics of the southern basin of Tauranga Harbour

The circulation of the southern basin of Tauranga Harbour was simulated using a 3-D hydrodynamic model ELCOM. A 9-day field campaign in 1999 provided data on current velocity, temperature and salinity profiles at three stations within the main basin. The tidal wave changed most in amplitude and speed in the constricted entrances to channels, for example the M2 tide attenuated by 10% over 500 m at the main entrance, and only an additional 17% over the 15 km to the top of the southern basin. The modelled temperature was sensitive to wind mixing, particularly in tidal flat regions. Residence times ranged from 3 to 8 days, with higher residence times occurring in sub-estuaries with constricted mouths. The typical annual storm events were predicted to reduce the residence times by 24%–39% depending on season. Model scenarios of storm discharge events in the Wairoa River varying from 41.69 m3/s to 175.9 m3/s show that these events can cause salinity gradients across the harbour of up to 4 PSU

Probing dynamics of an electron-spin ensemble via a superconducting resonator

We study spin relaxation and diffusion in an electron-spin ensemble of nitrogen impurities in diamond at low temperature (0.25-1.2 K) and polarizing magnetic field (80-300 mT). Measurements exploit mode- and temperature-dependent coupling of hyperfine-split sub-ensembles to the resonator. Temperature-independent spin linewidth and relaxation time suggest that spin diffusion limits spin relaxation. Depolarization of one sub-ensemble by resonant pumping of another indicates fast cross-relaxation compared to spin diffusion, with implications on use of sub-ensembles as independent quantum memories.Comment: 5 pages, 5 figures, and Supplementary Information (2 figures

The High Frequency Instrument of Planck: Requirements and Design

The Planck satellite is a project of the European Space Agency based on a wide international collaboration, including United States and Canadian laboratories. It is dedicated to the measurement of the anisotropy of the Cosmic Microwave Background (CMB) with unprecedented sensitivity and angular resolution. The detectors of its High frequency Instrument (HFI) are bolometers cooled down to 100 mK. Their sensitivity will be limited by the photon noise of the CMB itself at low frequencies, and of the instrument background at high frequencies. The requirements on the measurement chain are directly related to the strategy of observation used for the satellite. Due to the scanning on the sky, time features of the measurement chain are directly transformed into angular features in the sky maps. This impacts the bolometer design as well as other elements: For example, the cooling system must present outstanding temperature stability, and the amplification chain must show, down to very low frequencies, a flat noise spectrum

Use of High Sensitivity Bolometers for Astronomy: Planck High Frequency Instrument

The Planck satellite is dedicated to the measurement of the anisotropy of the Cosmic Microwave Background (CMB) with unprecedented sensitivity and angular resolution. It is a project of the European Space Agency based on a wide international collaboration, including United States and Canadian laboratories. The detectors of its High Frequency Instrument (HFI) are bolometers cooled down to 100 mK. Their sensitivity will be limited by the photon noise of the CMB itself at low frequencies, and of the instrument background at high frequencies. The requirements on the measurement chain are directly related to the strategy of observation used for the satellite. This impacts the bolometer design as well as other elements: The cooling system must present outstanding temperature stability, and the amplification chain must show a flat noise spectrum down to very low frequencies

Realization of microwave quantum circuits using hybrid superconducting-semiconducting nanowire Josephson elements

We report the realization of quantum microwave circuits using hybrid superconductor-semiconductor Josephson elements comprised of InAs nanowires contacted by NbTiN. Capacitively-shunted single elements behave as transmon qubits with electrically tunable transition frequencies. Two-element circuits also exhibit transmon-like behavior near zero applied flux, but behave as flux qubits at half the flux quantum, where non-sinusoidal current-phase relations in the elements produce a double-well Josephson potential. These hybrid Josephson elements are promising for applications requiring microwave superconducting circuits operating in magnetic field.Comment: Main text: 4 pages, 4 figures; Supplement: 10 pages, 8 figures, 1 tabl

A useful form of the recurrence relation between relativistic atomic matrix elements of radial powers

Recently obtained recurrence formulae for relativistic hydrogenic radial matrix elements are cast in a simpler and perhaps more useful form. This is achieved with the help of a new relation between the $r^a$ and the $\beta r^b$ terms ($\beta$ is a $4\times 4$ Dirac matrix and $a, b$ are constants) in the atomic matrix elements.Comment: 7 pages, no figure

New non-unitary representations in a Dirac hydrogen atom

New non-unitary representations of the SU(2) algebra are introduced for the case of the Dirac equation with a Coulomb potential; an extra phase, needed to close the algebra, is also introduced. The new representations does not require integer or half integer labels. The set of operators defined are used to span the complete space of bound state eigenstates of the problem thus solving it in an essentially algebraic way

Recurrence relation for relativistic atomic matrix elements

Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.Comment: 10 pages, no figure

The trispectrum of the Cosmic Microwave Background on sub-degree angular scales: an analysis of the BOOMERanG data

The trispectrum of the cosmic microwave background can be used to assess the level of non-Gaussianity on cosmological scales. It probes the fourth order moment, as a function of angular scale, of the probability distribution function of fluctuations and has been shown to be sensitive to primordial non-gaussianity, secondary anisotropies (such as the Ostriker-Vishniac effect) and systematic effects (such as astrophysical foregrounds). In this paper we develop a formalism for estimating the trispectrum from high resolution sky maps which incorporates the impact of finite sky coverage. This leads to a series of operations applied to the data set to minimize the effects of contamination due to the Gaussian component and correlations between estimates at different scales. To illustrate the effect of the estimation process, we apply our procedure to the BOOMERanG data set and show that it is consistent with Gaussianity. This work presents the first estimation of the CMB trispectrum on sub-degree scales.Comment: 14 pages, submitted to MNRA