Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page

Electron capture from helium by photons

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Macular Bioaccelerometers on Earth and in Space

Space flight offers the opportunity to study linear bioaccelerometers (vestibular maculas) in the virtual absence of a primary stimulus, gravitational acceleration. Macular research in space is particularly important to NASA because the bioaccelerometers are proving to be weighted neural networks in which information is distributed for parallel processing. Neural networks are plastic and highly adaptive to new environments. Combined morphological-physiological studies of maculas fixed in space and following flight should reveal macular adaptive responses to microgravity, and their time-course. Ground-based research, already begun, using computer-assisted, 3-dimensional reconstruction of macular terminal fields will lead to development of computer models of functioning maculas. This research should continue in conjunction with physiological studies, including work with multichannel electrodes. The results of such a combined effort could usher in a new era in understanding vestibular function on Earth and in space. They can also provide a rational basis for counter-measures to space motion sickness, which may prove troublesome as space voyager encounter new gravitational fields on planets, or must re-adapt to 1 g upon return to earth

Generalized Background-Field Method

The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than the ordinary background-field gauge, in that even the triple-gluon vertices for internal lines contain only four terms, not the usual six. This reduction simplifies the calculation inspite of the necessity to include other vertices for compensation. Like the ordinary background-field gauge, this generalized background-field gauge also preserves gauge invariance of the external particles. As a check of the result and an illustration for the reduction in labour, an explicit calculation of the two-loop QCD $\beta$-function is carried out in this new gauge. It results in a saving of 45% of computation compared to the ordinary background-field gauge.Comment: 17 pages, Latex, 18 figures in Postscrip

A mirrorless spinwave resonator

Optical resonance is central to a wide range of optical devices and techniques. In an optical cavity, the round-trip length and mirror reflectivity can be chosen to optimize the circulating optical power, linewidth, and free-spectral range (FSR) for a given application. In this paper we show how an atomic spinwave system, with no physical mirrors, can behave in a manner that is analogous to an optical cavity. We demonstrate this similarity by characterising the build-up and decay of the resonance in the time domain, and measuring the effective optical linewidth and FSR in the frequency domain. Our spinwave is generated in a 20 cm long Rb gas cell, yet it facilitates an effective FSR of 83 kHz, which would require a round-trip path of 3.6 km in a free-space optical cavity. Furthermore, the spinwave coupling is controllable enabling dynamic tuning of the effective cavity parameters.Comment: 13 pages, 4 figure

A quantum study of multi-bit phase coding for optical storage

We propose a scheme which encodes information in both the longitudinal and spatial transverse phases of a continuous-wave optical beam. A split detector-based interferometric scheme is then introduced to optimally detect both encoded phase signals. In contrast to present-day optical storage devices, our phase coding scheme has an information storage capacity which scales with the power of the read-out optical beam. We analyse the maximum number of encoding possibilities at the shot noise limit. In addition, we show that using squeezed light, the shot noise limit can be overcome and the number of encoding possibilities increased. We discuss a possible application of our phase coding scheme for increasing the capacities of optical storage devices.Comment: 8 pages, 7 figures (Please email author for a PDF file if the manuscript does not turn out properly

Systematic and Stochastic Variations in Pulsar Dispersion Measures

We analyze deterministic and random temporal variations in dispersion measure (DM) from the full three-dimensional velocities of pulsars with respect to the solar system, combined with electron-density variations on a wide range of length scales. Previous treatments have largely ignored the pulsar's changing distance while favoring interpretations involving the change in sky position from transverse motion. Linear trends in pulsar DMs seen over 5-10~year timescales may signify sizable DM gradients in the interstellar medium (ISM) sampled by the changing direction of the line of sight to the pulsar. We show that motions parallel to the line of sight can also account for linear trends, for the apparent excess of DM variance over that extrapolated from scintillation measurements, and for the apparent non-Kolmogorov scalings of DM structure functions inferred in some cases. Pulsar motions through atomic gas may produce bow-shock ionized gas that also contributes to DM variations. We discuss possible causes of periodic or quasi-periodic changes in DM, including seasonal changes in the ionosphere, annual variation of the solar elongation angle, structure in the heliosphere-ISM boundary, and substructure in the ISM. We assess the solar cycle's role on the amplitude of ionospheric and solar-wind variations. Interstellar refraction can produce cyclic timing variations from the error in transforming arrival times to the solar system barycenter. We apply our methods to DM time series and DM gradient measurements in the literature and assess consistency with a Kolmogorov medium. Finally, we discuss the implications of DM modeling in precision pulsar timing experiments.Comment: 24 pages, 17 figures, published in Ap