Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates

The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates (BEC) by solving the Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both the BdG and TDGP approaches allows one to unambiguously identify every observed mode.Comment: 5 pages, 4 figure

Husimi Transform of an Operator Product

It is shown that the series derived by Mizrahi, giving the Husimi transform (or covariant symbol) of an operator product, is absolutely convergent for a large class of operators. In particular, the generalized Liouville equation, describing the time evolution of the Husimi function, is absolutely convergent for a large class of Hamiltonians. By contrast, the series derived by Groenewold, giving the Weyl transform of an operator product, is often only asymptotic, or even undefined. The result is used to derive an alternative way of expressing expectation values in terms of the Husimi function. The advantage of this formula is that it applies in many of the cases where the anti-Husimi transform (or contravariant symbol) is so highly singular that it fails to exist as a tempered distribution.Comment: AMS-Latex, 13 page

A Computer Simulation of the Oxygen Reduction Reaction in Carbonate Melts

A computer simulation of the oxygen reduction reaction in various carbonate melts has been carried out under steady-state conditions on the basis of a proposed kinetic model which takes into consideration the autocatalytic reaction involving oxygen and other reducible oxygen species in the melt, and the neutralization of oxide ions by dissolved carbon dioxide. A simulation of the presence of (physically) dissolved oxygen, in the diffusion layer region of the melt, corresponding to the possible situation in porous electrodes, causes a significant enhancement in the polarization curves, particularly in the mass-transfer control region. On the other hand, high levels of dissolved CO2 in the melt reduce the current density in the mass-transfer control region by reducing the concentration of active dioxygen ions, but enhance it considerably in the kinetic limiting (CO2 neutralization) region. High rates of the autocatalytic and neutralization reactions display the same effects on the polarization curves as dissolved O2 and CO2, respectively, but to a lesser degree. Comparison of the simulated polarization curves in various carbonate melts indicates that Li-rich melts show the best kinetic performance. On the contrary, the highest limiting currents are observed in K- or Na-rich melts. Variation of the cation composition in Li/K carbonate melts indicates that melts of high Li-content should give better kinetic performance

Lateral stress evolution in chromium sulfide cermets with varying excess chromium

The shock response of chromium sulfide-chromium, a cermet of potential interest as a matrix material for ballistic applications, has been investigated at two molar ratios. Using a combustion synthesis technique allowed for control of the molar ratio of the material, which was investigated under near-stoichiometric (cermet) and excess chromium (interpenetrating composite) conditions, representing chromium:sulfur molar ratios of 1.15:1 and 4:1, respectively. The compacts were investigated via the plate-impact technique, which allowed the material to be loaded under a onedimensional state of strain. Embedded manganin stress gauges were employed to monitor the temporal evolution of longitudinal and lateral components of stress in both materials. Comparison of these two components has allowed assessment of the variation of material shear strength both with impact pressure/strain-rate and time for the two molar ratio conditions. The two materials exhibited identical material strength despite variations in their excess chromium content

Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process

The accuracy of the Arthurs-Kelly model of a simultaneous measurement of position and momentum is analysed using concepts developed by Braginsky and Khalili in the context of measurements of a single quantum observable. A distinction is made between the errors of retrodiction and prediction. It is shown that the distribution of measured values coincides with the initial state Husimi function when the retrodictive accuracy is maximised, and that it is related to the final state anti-Husimi function (the P representation of quantum optics) when the predictive accuracy is maximised. The disturbance of the system by the measurement is also discussed. A class of minimally disturbing measurements is characterised. It is shown that the distribution of measured values then coincides with one of the smoothed Wigner functions described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final published versio

Retrodictively Optimal Localisations in Phase Space

In a previous paper it was shown that the distribution of measured values for a retrodictively optimal simultaneous measurement of position and momentum is always given by the initial state Husimi function. This result is now generalised to retrodictively optimal simultaneous measurements of an arbitrary pair of rotated quadratures x_theta1 and x_theta2. It is shown, that given any such measurement, it is possible to find another such measurement, informationally equivalent to the first, for which the axes defined by the two quadratures are perpendicular. It is further shown that the distribution of measured values for such a meaurement belongs to the class of generalised Husimi functions most recently discussed by Wuensche and Buzek. The class consists of the subset of Wodkiewicz's operational probability distributions for which the filter reference state is a squeezed vaccuum state.Comment: 11 pages, 2 figures. AMS Latex. Replaced with published versio

Pelletizing

DURING the last 15 or 20 years we have witnessed an extra-ordinary increase in the quantity of artificial agglomera-tes used in blast-furnace burdens. This expansion has occurred in two fields, the first being sintering, a technique applied particularly to the agglomeration of low grade 'earthy' ores and to screenings from high quality Jump

Control of quantum interference in the quantum eraser

We have implemented an optical quantum eraser with the aim of studying this phenomenon in the context of state discrimination. An interfering single photon is entangled with another one serving as a which-path marker. As a consequence, the visibility of the interference as well as the which-path information are constrained by the overlap (measured by the inner product) between the which-path marker states, which in a more general situation are non-orthogonal. In order to perform which-path or quantum eraser measurements while analyzing non-orthogonal states, we resort to a probabilistic method for the unambiguous modification of the inner product between the two states of the which-path marker in a discrimination-like process.Comment: Submitted to New Journal of Physics, March 200

Diet and risk of diverticular disease in Oxford cohort of European Prospective Investigation into Cancer and Nutrition (EPIC): prospective study of British vegetarians and non-vegetarians

Objective To examine the associations of a vegetarian diet and dietary fibre intake with risk of diverticular disease