Task scheduling for a real time multiprocessor

Algorithm for scheduling real time tasks in multiprocessing syste

(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory

In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum mechanics," Pascual Jordan (1927b,g) presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. As an alternative that avoids the mathematical difficulties facing the approach of Jordan and Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert space formalism of quantum mechanics. In this paper, we focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identication of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identication of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan (1927b) was the first to state those rules in full generality. Von Neumann (1927a) rephrased them and, in a subsequent paper (von Neumann, 1927b), sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics.Comment: New version. The main difference with the old version is that the introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has been accepted for publication in European Physical Journal

Effects of urbanisation and landscape heterogeneity mediated by feeding guild and body size in a community of coprophilous beetles

Although the impacts of urbanisation on biodiversity are well studied, the precise response of some invertebrate groups remains poorly known. Dung-associated beetles are little studied in an urban context, especially in temperate regions. We considered how landscape heterogeneity, assessed at three spatial scales (250, 500 and 1000 metre radius), mediates the community composition of coprophilous beetles on a broad urban gradient. Beetles were sampled using simple dung-baited traps, placed at 48 sites stratified across three distance bands around a large urban centre in England. The most urban sites hosted the lowest abundance of saprophagous beetles, with a lower mean body length relative to the least urban sites. Predicted overall species richness and the richness of saprophagous species were also lowest at the most urban sites. Ordination analyses followed by variation partitioning revealed that landscape heterogeneity across the urban gradient explained a small but significant proportion of community composition. Heterogeneity data for a 500-metre radius around each site provided the best fit with beetle community data. Larger saprophagous species were associated with lower amounts of manmade surface and improved grassland. Some individual species, particularly predators, appeared to be positively associated with urban or urban fringe sites. This study is probably the first to examine the response of the whole coprophilous beetle community to urbanisation. Our results suggest that the response of this community to urbanisation matches expectations based on other taxonomic groups, whilst emphasising the complex nature of this response, with some smaller-bodied species potentially benefitting from urbanisation

Parity meter for charge qubits: an efficient quantum entangler

We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of a controlled NOT gate.Comment: 8 pages, 4 figures; v2: discussion of measurement time, references adde

Temporal variations in scattering and dispersion measure in the Crab Pulsar and their effect on timing precision

We have measured variations in scattering time scales in the Crab Pulsar over a 30-year period, using observations made at 610 MHz with the 42-ft telescope at Jodrell Bank Observatory. Over more recent years, where regular Lovell Telescope observations at frequencies around 1400 MHz were available, we have also determined the dispersion measure variations, after disentangling the scattering delay from the dispersive delay. We demonstrate a relationship between scattering and dispersion measure variations, with a correlation coefficient of $0.56\pm0.01$. The short time scales over which these quantities vary, the size of the variations, and the close correlation between scattering and dispersion measure all suggest that the effects are due to discrete structures within the Crab Nebula, with size scales of $\sim6$ AU (corresponding to an angular size of $\sim2$ mas at an assumed distance of 2200 pc). We mitigate the effects of scattering on the observed pulse shape by using the measured scattering information to modify the template used for generating the pulse arrival times, thus improving the precision to which the pulsar can be timed. We test this on timing data taken during periods of high scattering, and obtain a factor of two improvement in the root mean square of the timing residuals.Comment: 10 pages, 7 figures. Accepted for publication in MNRA

Chiral Spin Textures of Strongly Interacting Particles in Quantum Dots

We probe for statistical and Coulomb induced spin textures among the low-lying states of repulsively-interacting particles confined to potentials that are both rotationally and time-reversal invariant. In particular, we focus on two-dimensional quantum dots and employ configuration-interaction techniques to directly compute the correlated many-body eigenstates of the system. We produce spatial maps of the single-particle charge and spin density and verify the annular structure of the charge density and the rotational invariance of the spin field. We further compute two-point spin correlations to determine the correlated structure of a single component of the spin vector field. In addition, we compute three-point spin correlation functions to uncover chiral structures. We present evidence for both chiral and quasi-topological spin textures within energetically degenerate subspaces in the three- and four-particle system.Comment: 13 pages, 17 figures, 1 tabl

Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology

Scalar-Tensor theories of gravity can be formulated in different frames, most notably, the Einstein and the Jordan one. While some debate still persists in the literature on the physical status of the different frames, a frame transformation in Scalar-Tensor theories amounts to a local redefinition of the metric, and then should not affect physical results. We analyze the issue in a cosmological context. In particular, we define all the relevant observables (redshift, distances, cross-sections, ...) in terms of frame-independent quantities. Then, we give a frame-independent formulation of the Boltzmann equation, and outline its use in relevant examples such as particle freeze-out and the evolution of the CMB photon distribution function. Finally, we derive the gravitational equations for the frame-independent quantities at first order in perturbation theory. From a practical point of view, the present approach allows the simultaneous implementation of the good aspects of the two frames in a clear and straightforward way.Comment: 15 pages, matches version to be published on Phys. Rev.

Homogenization induced by chaotic mixing and diffusion in an oscillatory chemical reaction

A model for an imperfectly mixed batch reactor with the chlorine dioxide-iodine-malonic acid (CDIMA) reaction, with the mixing being modelled by chaotic advection, is considered. The reactor is assumed to be operating in oscillatory mode and the way in which an initial spatial perturbation becomes homogenized is examined. When the kinetics are such that the only stable homogeneous state is oscillatory then the perturbation is always entrained into these oscillations. The rate at which this occurs is relatively insensitive to the chemical effects, measured by the Damkohler number, and is comparable to the rate of homogenization of a passive contaminant. When both steady and oscillatory states are stable, spatially homogeneous states, two possibilities can occur. For the smaller Damkohler numbers, a localized perturbation at the steady state is homogenized within the background oscillations. For larger Damkohler numbers, regions of both oscillatory and steady behavior can co-exist for relatively long times before the system collapses to having the steady state everywhere. An interpretation of this behavior is provided by the one-dimensional Lagrangian filament model, which is analyzed in detail

Phase-resolved far-ultraviolet HST spectroscopy of the peculiar magnetic white dwarf RE J0317-853

We present phase resolved FUV HST FOS spectra of the rapidly rotating, highly magnetic white dwarf RE J0317-853. Using these data, we construct a new model for the magnetic field morphology across the stellar surface. From an expansion into spherical harmonics, we find the range of magnetic field strengths present is 180-800MG. For the first time we could identify an absorption feature present at certain phases at 1160A as a ``forbidden'' 1s_0 -> 2s_0 component, due to the combined presence of an electric and magnetic field.Comment: 15 pages including 4 figures. Accepted for publication in ApJ Letter

Symmetric three-particle motion in Stokes flow: equilibrium for heavy spheres in contrast to "end-of-world" for point forces

A stationary stable solution of the Stokes equations for three identical heavy solid spheres falling in a vertical plane is found. It has no analog in the point-particle approximation. Three spheres aligned horizontally at equal distances evolve towards the equilibrium relative configuration while the point particles collapse onto a single point in a finite time.Comment: 4 pages, 7 figure