Unit Quaternions and the Bloch Sphere

The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unitary transformations, providing a simpler (essentially classical) analysis of time-reversal. But the quaternion viewpoint also reveals a surprisingly large broken symmetry, as well as a potential way to restore it, via a natural expansion of the state space that has parallels to second order fermions. This expansion to "second order qubits" would imply either a larger gauge freedom or a natural space of hidden variables.Comment: 25 pages, 1 figure; Referee-inspired improvements; accepted for publication in J. Phys.

Simulation of the Gravsat/Geopause mission

A simulation of the proposed low Gravsat and high Geopause satellite mission is presented. This mission promises fundamental improvements in the accuracy of low order geopotential coefficients by using satellite-to-satellite tracking technology coupled with a global sampling of the gravity field. Ten days of data from six stations are assumed. A drag compensation system for the low satellite is also postulated. The results show a one to two order of magnitude improvement in the accuracy of the low order coefficients through degree 8 and order 6. These results are easily adjusted to reflect a different data accuracy level and low satellite altitude

Effects of local event-by-event conservation laws in ultrarelativistic heavy-ion collisions at particlization

Many simulations of relativistic heavy-ion collisions involve the switching from relativistic hydrodynamics to kinetic particle transport. This switching entails the sampling of particles from the distribution of energy, momentum, and conserved currents provided by hydrodynamics. Usually, this sampling ensures the conservation of these quantities only on the average, i.e., the conserved quantities may actually fluctuate among the sampled particle configurations and only their averages over many such configurations agree with their values from hydrodynamics. Here we apply a recently invented method [D. Oliinychenko and V. Koch, Phys. Rev. Lett. 123, 182302 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.182302] to ensure conservation laws for each sampled configuration in spatially compact regions (patches) and study their effects: From the well-known (micro-)canonical suppression of means and variances to little studied (micro-)canonical correlations and higher-order fluctuations. Most of these effects are sensitive to the patch size. Many of them do not disappear even in the thermodynamic limit, when the patch size goes to infinity. The developed method is essential for particlization of stochastic hydrodynamics. It is useful for studying the chiral magnetic effect, small systems, and in general for fluctuation and correlation observables

Long and short arc altitude determination for GEOS-C

The accuracy with which the GEOS-C altitude may be estimated over long (7 day) and short (40 minute) orbital arcs is investigated. Over the long are excellent agreement was attained between a simulation of the orbit determination process and a covariance analysis. Both approaches yielded RMS altitude errors of about 1.5 meters over the Caribbean calibration area and approximately 7.5 meters overall. The geopotential was identified as the largest error source. For the short arc, the covariance analysis revealed that the propagated altitude error is linearly dependent upon station survey component errors which are also the largest source of altitude errors. An Appendix contains the mathematics of covariance analysis as applied to orbit determination

Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

Two-dimensional Valence Bond Solid (AKLT) states from t2gt_{2g} electrons

Two-dimensional AKLT model on a honeycomb lattice has been shown to be a universal resource for quantum computation. In this valence bond solid, however, the spin interactions involve higher powers of the Heisenberg coupling $(\vec{S}_i \cdot \vec{S}_j)^n$, making these states seemingly unrealistic on bipartite lattices, where one expects a simple antiferromagnetic order. We show that those interactions can be generated by orbital physics in multiorbital Mott insulators. We focus on $t_{2g}$ electrons on the honeycomb lattice and propose a physical realization of the spin-$3/2$ AKLT state. We find a phase transition from the AKLT to the Neel state on increasing Hund's rule coupling, which is confirmed by density matrix renormalization group (DMRG) simulations. An experimental signature of the AKLT state consists of protected, free spins-1/2 on lattice vacancies, which may be detected in the spin susceptibility

The use of accruals to manage reported earnings: theory and evidence

This paper develops a model in which firm managers maximize their own compensation by using accruals to manage reported earnings. The results of the model suggest that the form of the managerial compensation function and managerial time preferences may have an important influence on the relationship between accruals and latent earnings. Among the possible relationships suggested by the model are strategies we call Smooth Income, Occasional Big Bath, Live for Today, and Maximize Variability, each of which suggests a different reporting strategy pursued by managers. Most empirical tests of accruals are inconsistent with this and other theoretical models because they include a single earnings variable in a linear regression analysis. Instead, we document the reporting of accruals by two firms, Sunbeam and Citicorp, that is consistent with the “Live for Today” and “Occasional Big Bath” strategies.Investments

Infrared measurements of spacecraft glow planned for Spacelab 2

A liquid helium cooled infrared telescope (IRT) was to be flown in July 1985 on Spacelab 2. The instrument is designed to measure both diffuse and discrete infrared astronomical sources, including the zodiacal light, galactic, and extragalactic components, as well as to evaluate the induced Orbiter environment. The focal plane contains ten photoconductive detectors covering six broad bands from 2 to 120 microns. Each detector has a 0.5 by 1.0 deg field of view optimized for detection of extended sources of IR radiation. Except for the 2 micron detector, the system noise is limited by the sky background noise. The measurements planned for the IRT use the 1 meter base of the Plasma Diagnostic Package (PDP), an already existing SL 2 experiment, as the glow generating surface. The measurements are repeated changing the position of the PDP, the attitude of the Orbiter, and the ram direction in an effort to remove both the thermal component of the PDP emission and the cosmic background radiation

Nimbus 6 Doppler processing using the Fairbanks calibration platform

A weighted least squares processor is examined. Research conducted in support of the NASA satellite aided Search and Rescue program is presented. An estimated NIMBUS 6 ephemeris, accurate to 1.5-2.5 km and 0.5-2.5 m/s relative to a reference orbit, is obtained during the three day signal transmission period. This suggests updating the knowledge of the relay satellite ephemeris by one reference beacon is needed during the Search and Rescue demonstration

Detection of Other Planetary Systems Using Photometry

Detection of extrasolar short-period planets, particularly if they are in the liquid-water zone, would be one of the most exciting discoveries of our lifetime. A well-planned space mission has the capability of making this discovery using the photometric method. An Earth-sized planet transiting a Sun-like star will cause a decrease in the apparent luminosity of the star by one part in 10,000 with a duration of about 12 hours and a period of about one year. Given a random orientation of orbital plane alignments with the line-of-sight to a star, and assuming our solar system to be typical, one would expect 1 percent of the stars monitored to exhibit planetary transits. A null result would also be significant and indicate that Earth-sized planets are rare. For the mission to be successful one needs a sensor system that can simultaneously monitor many thousands of stars with a photometric precision of one part in 30,000 per hour of integration. Confirmation of a detection will involve detection of a second transit that will yield a period and predict the time for a third and subsequent transits. The technology issues that need to be addressed are twofold: one is for an appropriate optical design; the other is for a detector system with the necessary photometric precision. Two candidates for the detector system are silicon diodes and CCD's