Binary Dynamics through the Fifth Power of Spin at O ( G 2 )
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The quantum Hall effect is the birthplace of topological states of matter, a major theme at the forefront of condensed matter physics in the past two decades. The fractional quantum Hall (FQH) effect revolutionized our understanding of phases of electronic matter. FQH states support exotic fractionally charged excitations that obey Abelian or non-Abelian fractional statistics, which are topological excitations that result from the underlying topological order. During this project, our group discovered a previously unrecognized geometric degree of freedom of incompressible FQH states and studied that for a variety of gapped FQH states. We brought this new concept into direct contact with experiments for the first time by generalizing it to Fermi-liquid states of composite fermions. Using the newly formulated powerful infinite Density Matrix Renormalization Group method, our numerical calculations yielded a parameter free prediction that was found to be in excellent agreement with experimental findings on electron systems in semiconductor heterostructures. In parallel, we performed extensive numerical studies on different, competing phases at various Landau level filling factors, and quantum phase transitions that result from such a competition, e.g. Abelian-non-Abelian phase transitions in bilayer systems. We studied geometrical excitations dubbed “gravitons” (because of their analogy with excitations in the theory of gravitation) and ways to excite and detect them, and explored how they couple with topological excitations. In graphene-based chiral materials, we realized the ability to tune through different incompressible and compressible states in a single Landau level, and found appropriate experimental parameters for the exploration of universal Luttinger liquid behavior not obtained in semiconductor-based electron systems. We showed that topological systems had a very different response from nontopological systems to strong disorder (many-body localization) as well as periodic drives.
Gravitational theoretical implications of geodetic satellite field measurements
Elliptic Kruskal-Schwarzschild space, discussing identification of points which limit Kruskal space into Minkowski space
Gravitation research - experimental test of Freundlich red-shift hypothesis and measurement of metastable vs ground-state electron exchange cross sections for helium and neon
One-dimensional model describing stellar motion for studying relaxation of self-gravitating gas
Relaxation of two-component self-gravitating gas
Gravitational experiments with evolution of two-dimensional cylindrical galaxy
Errors from lunar ephemeris defects found through lunar motion numerical integrations to affect data analyses from spacecraft and ephemeris time determination
Residuals in lunar ephemeris calculated from Brown theory confirmed by lunar probes radio tracking and reduced by repeated calculations, using LE 5
Gravitational relativistic theory tests using tracking data from interplanetary spacecraft, orbiters and landers
Gravitational lunar theory high order solution for geophysical relevance, discussing perturbation methods and computer analyzed ephemeris time
With data from two or more well-located observing stations, the lunar range can be corrected accurately for the effects of polar motion and fluctuations in the earth's rotation rate. Very accurate corrections can be made for the earth tides at each station. It appears that the use of lasers giving roughly 0.1-msec pulse lengths is highly desirable. With them, single-shot ranging accuracies of about 3 cm are expected. The actual lunar range results will be analyzed by fitting a numerical integration for the lunar motion to the data. A mathematical model for lunar range is given. Tests of the theory of gravitation are considered.
The uses of radar observations of planets and very-long-baseline radio interferometric observations of extragalactic objects to test theories of gravitation are described in detail with special emphasis on sources of error. The accuracy achievable in these tests with data already obtained, can be summarized in terms of: retardation of signal propagation (radar), deflection of radio waves (interferometry), advance of planetary perihelia (radar), gravitational quadrupole moment of sun (radar), and time variation of gravitational constant (radar). The analyses completed to date have yielded no significant disagreement with the predictions of general relativity.
The theory of gravitational accretion of the terrestrial planets is examined. The concept of a 'closed feeding zone' is somewhat unrealistic, but provides a lower bound on the accretion time. A velocity relation for planetesimals which includes an initial velocity component is suggested. The orbital parameters of the planetesimals and the dimensions of the feeding zone are related to their relative velocities. The assumption of an initial velocity does not seriously change the accretion time. Mercury, Venus, and the earth have accretion times on the order of 100 million years. Mars requires well over one billion years to accrete by the same assumptions. The lunar cratering history makes a late formation of Mars unlikely. If Mars is as old as the earth, nongravitational forces or a violation of the feeding zone concept is required. One such possibility is the removal of matter from the zone of Mars by Jupiter's influence. The final sweeping up by Mars would result in the scattering of a considerable mass among the other terrestrial planets. The late postaccretional bombardments inferred for the moon and Mercury may have had this source.
The general theory of tides is developed within the framework of Einstein's theory of gravitation. It is based on the concept of Fermi frame and the associated notion of tidal frame along an open curve in spacetime. Following the previous work of the author an approximate scheme for the evaluation of tidal gravitational radiation is presented which is valid for weak gravitational fields. The emission of gravitational radiation from a body in the field of a black hole is discussed, and for some cases of astrophysical interest estimates are given for the contributions of radiation due to center-of-mass motion, purely tidal deformation, and the interference between the center of mass and tidal motions.
Milgrom's recent revision of Newtonian dynamics was introduced to eliminate the inference that large quantities of invisible mass exist in galaxies. Simple examples show that a Milgrom acceleration, in the form presented so far, imply other far-reaching changes in dynamics. The momentum of an isolated system is not conserved, and the usual theorem for center-of-mass motion of any system does not hold. Naive applications require extreme caution. The model fails to provide a complete description of particle dynamics and should be thought of as a revision of Kepler's laws rather than Newton's. The Milgrom acceleration also implies fundamental changes in cosmology. A quasi-Newtonian calculation adapted from Newtonian cosmology suggests that a Milgrom universe will recollapse even if the classical closure parameter theta is less than 1. The solution, however, fails to satisfy the cosmological principle. Reasons for the breakdown of this calculation are examined. A theory of gravitation needed before the behavior of a Milgrom universe can be predicted.