Covariant Calculation of General Relativistic Effects in an Orbiting Gyroscope Experiment

We carry out a covariant calculation of the measurable relativistic effects in an orbiting gyroscope experiment. The experiment, currently known as Gravity Probe B, compares the spin directions of an array of spinning gyroscopes with the optical axis of a telescope, all housed in a spacecraft that rolls about the optical axis. The spacecraft is steered so that the telescope always points toward a known guide star. We calculate the variation in the spin directions relative to readout loops rigidly fixed in the spacecraft, and express the variations in terms of quantities that can be measured, to sufficient accuracy, using an Earth-centered coordinate system. The measurable effects include the aberration of starlight, the geodetic precession caused by space curvature, the frame-dragging effect caused by the rotation of the Earth and the deflection of light by the Sun.Comment: 7 pages, 1 figure, to be submitted to Phys. Rev.

Geodetic precession and frame dragging observed far from massive objects and close to a gyroscope

Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.Comment: 11 page

Analysis of Chiral Mean-Field Models for Nuclei

An analysis of nuclear properties based on a relativistic energy functional containing Dirac nucleons and classical scalar and vector meson fields is discussed. Density functional theory implies that this energy functional can include many-body effects that go beyond the simple Hartree approximation. Using basic ideas from effective field theory, a systematic truncation scheme is developed for the energy functional, which is based on an expansion in powers of the meson fields and their gradients. Chiral models are analyzed by considering specific lagrangians that realize the spontaneously broken chiral symmetry of QCD in different ways and by studying them at the Hartree level. Models that include a light scalar meson playing a dual role as the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon interaction, and which include a "Mexican-hat" potential, fail to reproduce basic ground-state properties of nuclei. In contrast, chiral models with a nonlinear realization of the symmetry are shown to contain the full flexibility inherent in the general energy functional and can therefore successfully describe nuclei.Comment: 47 pages, REVTeX 3.0 with epsf.sty, plus 12 figures in separate uuencoded compressed postscript fil

Electric dipole moments of Hg, Xe, Rn, Ra, Pu, and TlF induced by the nuclear Schiff moment and limits on time-reversal violating interactions

We have calculated the atomic electric dipole moments (EDMs) induced in ^{199}Hg, ^{129}Xe, ^{223}Rn, ^{225}Ra, and ^{239}Pu by their respective nuclear Schiff moments S. The results are (in units 10^{-17}S(e {fm}^{3})^{-1}e cm): d(^{199}Hg)=-2.8, d(^{129}Xe)=0.38, d(^{223}Rn)=3.3, d(^{225}Ra)=-8.5, d(^{239}Pu)=-11. We have also calculated corrections to the parity- and time-invariance-violating (P,T-odd) spin-axis interaction constant in TlF. These results are important for the interpretation of atomic and molecular experiments on EDMs in terms of fundamental P,T-odd parameters.Comment: 16 page

Student learning dispositions: Multidimensional profiles highlight important differences among undergraduate stem honors thesis writers

Various personal dimensions of students—particularly motivation, self-efficacy beliefs, and epistemic beliefs—can change in response to teaching, affect student learning, and be conceptualized as learning dispositions. We propose that these learning dispositions serve as learning outcomes in their own right; that patterns of interrelationships among these specific learning dispositions are likely; and that differing constellations (or learning disposition profiles) may have meaningful implications for instructional practices. In this observational study, we examine changes in these learning dispositions in the context of six courses at four institutions designed to scaffold undergraduate thesis writing and promote students’ scientific reasoning in writing in science, technology, engineering, and mathematics. We explore the utility of cluster analysis for generating meaningful learning disposition profiles and building a more sophisticated understanding of students as complex, multidimensional learners. For example, while students’ self-efficacy beliefs about writing and science increased across capstone writing courses on average, there was considerable variability at the level of individual students. When responses on all of the personal dimensions were analyzed jointly using cluster analysis, several distinct and meaningful learning disposition profiles emerged. We explore these profiles in this work and discuss the implications of this framework for describing developmental trajectories of students’ scientific identities. We thank Mine Çetinkaya-Rundel for her insights regarding our statistical analyses. This research was funded by National Science Foundation award DUE-1525602

Exact solutions of the radial Schrodinger equation for some physical potentials

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained.Comment: 13 page

Double-slit interference pattern from single-slit screen and its gravitational analogues

The double slit experiment (DSE) is known as an important cornerstone in the foundations of physical theories such as Quantum Mechanics and Special Relativity. A large number of different variants of it were designed and performed over the years. We perform and discuss here a new verion with the somewhat unexpected results of obtaining interference pattern from single-slit screen. This outcome, which shows that the routes of the photons through the array were changed, leads one to discuss it, using the equivalence principle, in terms of geodesics mechanics. We show using either the Brill's version of the canonical formulation of general relativity or the linearized version of it that one may find corresponding and analogous situations in the framework of general relativity.Comment: 51 pages, 12 Figures five of them contain two subfigures and thus the number of figures is 17, 1 Table. Some minor changes introduced, especially, in the reference

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Phenomenology of the Lense-Thirring effect in the Solar System

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in Astrophysics and Space Science (ApSS). Some uncited references in the text now correctly quoted. One reference added. A footnote adde

Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation

The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a nucleon interacts with other nucleons as well as with electrons. Nuclear structure calculations of the CP-odd nuclear Schiff moment are discussed using the shell model and other theoretical approaches. Results of the calculations of atomic electric dipole moments due to the interaction of the nuclear Schiff moment with the electrons and the P and time-reversal (T) symmetry violating tensor-pseudotensor electron-nucleus are elucidated using different relativistic many-body theories. The principles of the measurement of the electric dipole moments of diamagnetic atoms are outlined. Upper limits for the nuclear Schiff moment and tensor-pseudotensor coupling constant are obtained combining the results of atomic experiments and relativistic many-body theories. The coefficients for the different sources of CP violation have been estimated at the elementary particle level for all the diamagnetic atoms of current experimental interest and their implications for physics beyond the standard model is discussed. Possible improvements of the current results of the measurements as well as quantum chromodynamics, nuclear and atomic calculations are suggested.Comment: 46 pages, 19 tables and 16 figures. A review article accepted for EPJ