Quantum Uncertainty Considerations for Gravitational Lens Interferometry

The measurement of the gravitational lens delay time between light paths has relied, to date, on the source having sufficient variability to allow photometric variations from each path to be compared. However, the delay times of many gravitational lenses cannot be measured because the intrinsic source amplitude variations are too small to be detectable. At the fundamental quantum mechanical level, such photometric time stamps allow which-path knowledge, removing the ability to obtain an interference pattern. However, if the two paths can be made equal (zero time delay) then interference can occur. We describe an interferometric approach to measuring gravitational lens delay times using a quantum-eraser/restorer approach, whereby the time travel along the two paths may be rendered measurably equal. Energy and time being non-commuting observables, constraints on the photon energy in the energy-time uncertainty principle, via adjustments of the width of the radio bandpass, dictate the uncertainty of the time delay and therefore whether the path taken along one or the other gravitational lens geodesic is knowable. If one starts with interference, for example, which-path information returns when the bandpass is broadened (constraints on the energy are relaxed) to the point where the uncertainty principle allows a knowledge of the arrival time to better than the gravitational lens delay time itself, at which point the interference will disappear. We discuss the near-term feasibility of such measurements in light of current narrow-band radio detectors and known short time-delay gravitational lenses.Comment: 22 page

Discrete analogue computing with rotor-routers

Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is spread throughout the system). It is also possible to efficiently check that a computation has been carried out correctly in less time than the computation itself required, provided one has a certificate that can itself be computed by the rotor-router network. Rotor-router networks can be viewed as both discrete analogues of continuous linear systems and deterministic analogues of stochastic processes.Comment: To appear in Chaos Special Focus Issue on Intrinsic and Designed Computatio

Coherent-feedback quantum control with a dynamic compensator

I present an experimental realization of a coherent-feedback control system that was recently proposed for testing basic principles of linear quantum stochastic control theory [M. R. James, H. I. Nurdin and I. R. Petersen, to appear in IEEE Transactions on Automatic Control (2008), arXiv:quant-ph/0703150v2]. For a dynamical plant consisting of an optical ring-resonator, I demonstrate ~ 7 dB broadband disturbance rejection of injected laser signals via all-optical feedback with a tailored dynamic compensator. Comparison of the results with a transfer function model pinpoints critical parameters that determine the coherent-feedback control system's performance.Comment: 4 pages, 4 EPS figure

Planetological implications of mass loss from the early Sun

The element lithium is observed to be underabundant in the Sun by a factor of approx. equal to 100. To account for this depletion, Boothroyd et al. (Ap. J., in press 1991) proposed a model in which the Sun's zero-age-main-sequence mass was approx. 1.1 solar magnitude. If this is the explanation for the lithium depletion, then astronomical observations of F/G dwarfs in clusters suggest that the timescale for mass loss is approx. equal to 0.6 Gyr. Assuming this approximate timescale, the authors investigated several planetological implications of the astrophysical model

VCE early acoustic test results of General Electric's high-radius ratio coannular plug nozzle

Results of variable cycle engine (VCE) early acoustic engine and model scale tests are presented. A summary of an extensive series of far field acoustic, advanced acoustic, and exhaust plume velocity measurements with a laser velocimeter of inverted velocity and temperature profile, high radius ratio coannular plug nozzles on a YJ101 VCE static engine test vehicle are reviewed. Select model scale simulated flight acoustic measurements for an unsuppressed and a mechanical suppressed coannular plug nozzle are also discussed. The engine acoustic nozzle tests verify previous model scale noise reduction measurements. The engine measurements show 4 to 6 PNdB aft quadrant jet noise reduction and up to 7 PNdB forward quadrant shock noise reduction relative to a fully mixed conical nozzle at the same specific thrust and mixed pressure ratio. The influences of outer nozzle radius ratio, inner stream velocity ratio, and area ratio are discussed. Also, laser velocimeter measurements of mean velocity and turbulent velocity of the YJ101 engine are illustrated. Select model scale static and simulated flight acoustic measurements are shown which corroborate that coannular suppression is maintained in forward speed

Plenary Panel Discussion: Challenges and opportunities for the future of control

This panel reflects the scope and diversity of the unprecedented challenges and opportunities for the systems and controls community that has been created by several research themes from the basic sciences to advanced technologies. Connecting physical processes at multiple time and space scales in quantum, statistical, fluid, and solid mechanics, remains not only a central scientific challenge but also one with increasing technological implications. This is particular so in highly organized and nonequilibrium systems as in biology and nanotechnology, where interconnection, feedback, and dynamics are playing an increasingly central role

Rayleigh scattering in the transmission spectrum of HAT-P-18b

We have performed ground-based transmission spectroscopy of the hot Jupiter HAT-P-18b using the ACAM instrument on the William Herschel Telescope (WHT). Differential spectroscopy over an entire night was carried out at a resolution of $R \approx 400$ using a nearby comparison star. We detect a bluewards slope extending across our optical transmission spectrum which runs from 4750 to 9250\AA. The slope is consistent with Rayleigh scattering at the equilibrium temperature of the planet (852K). We do not detect enhanced sodium absorption, which indicates that a high-altitude haze is masking the feature and giving rise to the Rayleigh slope. This is only the second discovery of a Rayleigh scattering slope in a hot Jupiter atmosphere from the ground, and our study illustrates how ground-based observations can provide transmission spectra with precision comparable to the Hubble Space Telescope.Comment: 11 pages, 9 figures, accepted for publication in MNRA

Calculating effective resistances on underlying networks of association schemes

Recently, in Refs. \cite{jsj} and \cite{res2}, calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on stratification and Stieltjes function associated with the network, whereas in the latter one a recursive formula for effective resistances was given based on the Christoffel-Darboux identity. In this paper, evaluation of effective resistances on more general networks which are underlying networks of association schemes is considered, where by using the algebraic combinatoric structures of association schemes such as stratification and Bose-Mesner algebras, an explicit formula for effective resistances on these networks is given in terms of the parameters of corresponding association schemes. Moreover, we show that for particular underlying networks of association schemes with diameter $d$ such that the adjacency matrix $A$ possesses $d+1$ distinct eigenvalues, all of the other adjacency matrices $A_i$, $i\neq 0,1$ can be written as polynomials of $A$, i.e., $A_i=P_i(A)$, where $P_i$ is not necessarily of degree $i$. Then, we use this property for these particular networks and assume that all of the conductances except for one of them, say $c\equiv c_1=1$, are zero to give a procedure for evaluating effective resistances on these networks. The preference of this procedure is that one can evaluate effective resistances by using the structure of their Bose-Mesner algebra without any need to know the spectrum of the adjacency matrices.Comment: 41 page

A Dynamical Analysis of the Proposed Circumbinary HW Virginis Planetary System

In 2009, the discovery of two planets orbiting the evolved binary star system HW Virginis was announced, based on systematic variations in the timing of eclipses between the two stars. The planets invoked in that work were significantly more massive than Jupiter, and moved on orbits that were mutually crossing - an architecture which suggests that mutual encounters and strong gravitational interactions are almost guaranteed. In this work, we perform a highly detailed analysis of the proposed HW Vir planetary system. First, we consider the dynamical stability of the system as proposed in the discovery work. Through a mapping process involving 91,125 individual simulations, we find that the system is so unstable that the planets proposed simply cannot exist, due to mean lifetimes of less than a thousand years across the whole parameter space. We then present a detailed re-analysis of the observational data on HW Vir, deriving a new orbital solution that provides a very good fit to the observational data. Our new analysis yields a system with planets more widely spaced, and of lower mass, than that proposed in the discovery work, and yields a significantly greater (and more realistic) estimate of the uncertainty in the orbit of the outermost body. Despite this, a detailed dynamical analysis of this new solution similarly reveals that it also requires the planets to move on orbits that are simply not dynamically feasible. Our results imply that some mechanism other than the influence of planetary companions must be the principal cause of the observed eclipse timing variations for HW Vir. If the sys- tem does host exoplanets, they must move on orbits differing greatly from those previously proposed. Our results illustrate the critical importance of performing dynamical analyses as a part of the discovery process for multiple-planet exoplanetary systems.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Societ