3,895 research outputs found
A Spin Network Primer
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for
the quantum theory of geometry. These structures encompass a diverse range of
techniques which may be used in the quantum mechanics of finite dimensional
systems, gauge theory, and knot theory. Though accessible to undergraduates,
spin network techniques are buried in more complicated formulations. In this
paper a diagrammatic method, simple but rich, is introduced through an
association of 2 by 2 matrices to diagrams. This spin network diagrammatic
method offers new perspectives on the quantum mechanics of angular momentum,
group theory, knot theory, and even quantum geometry. Examples in each of these
areas are discussed.Comment: A review of spin networks suitable for students of advanced quantum
mechanics (undergraduate). 16 pages, many eps figures, to be published in Am.
J. Phys v2: Updated to include key referenc
Cosmological gravitomagnetism and Mach's principle
The spin axes of gyroscopes experimentally define local non-rotating frames.
But what physical cause governs the time-evolution of gyroscope axes? We
consider linear perturbations of Friedmann-Robertson-Walker cosmologies with
k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin
axes of gyroscopes relative to the directions of geodesics to quasars in the
asymptotic unperturbed FRW space? Using Cartan's formalism with local
orthonormal bases we cast the laws of linear cosmological gravitomagnetism into
a form showing the close correspondence with the laws of ordinary magnetism.
Our results, valid for any equation of state for cosmological matter, are: 1)
The dragging of a gyroscope axis by rotational perturbations of matter beyond
the Hubble-dot radius from the gyroscope is exponentially suppressed, where dot
is the derivative with respect to cosmic time. 2) If the perturbation of matter
is a homogeneous rotation inside some radius around a gyroscope, then exact
dragging of the gyroscope axis by the rotational perturbation is reached
exponentially fast as the rotation radius grows beyond the H-dot radius. 3) For
the most general linear cosmological perturbations the time-evolution of all
gyroscope spin axes exactly follow a weighted average of the energy currents of
cosmological matter. The weight function is the same as in Ampere's law except
that the inverse square law is replaced by the Yukawa force with the Hubble-dot
cutoff. Our results demonstrate (in first order perturbation theory for FRW
cosmologies with k = 0) the validity of Mach's hypothesis that axes of local
non-rotating frames precisely follow an average of the motion of cosmic matter.Comment: 18 pages, 1 figure. Comments and references adde
Theorem on the proportionality of inertial and gravitational masses in classical mechanics
We considered the problem of the proportionality of inertial and
gravitational masses in classical mechanics. We found that the kinetic energy
of a material mass point m in a circular motion with a constant angular
velocity around another material point M depends only on its gravitational
mass. This fact, together with the known result that the straight line is a
circumference with an infinite radius, allowed us to prove the proportionality
between the inertial and gravitational masses.Comment: ReVTeX file, 10p
On the stability of self-gravitating accreting flows
Analytic methods show stability of the stationary accretion of test fluids
but they are inconclusive in the case of self-gravitating stationary flows. We
investigate numerically stability of those stationary flows onto compact
objects that are transonic and rich in gas. In all studied examples solutions
appear stable. Numerical investigation suggests also that the analogy between
sonic and event horizons holds for small perturbations of compact support but
fails in the case of finite perturbations.Comment: 10 pages, accepted for publication in PR
Self-gravitating magnetised tori around black holes in general relativity
We investigate stationary, self-gravitating, magnetised disks (or tori)
around black holes. The models are obtained by numerically solving the coupled
system of the Einstein equations and the equations of ideal
general-relativistic magnetohydrodynamics. The mathematical formulation and
numerical aspects of our approach are similar to those reported in previous
works modeling stationary self-gravitating perfect-fluid tori, but the
inclusion of magnetic fields represents a new ingredient. Following previous
studies of purely hydrodynamical configurations, we construct our models
assuming Keplerian rotation in the disks and both spinning and spinless black
holes. We focus on the case of a toroidal distribution of the magnetic field
and build a large set of models corresponding to a wide range of values of the
magnetisation parameter, starting with weakly magnetised disks and ending at
configurations in which the magnetic pressure dominates over the thermal one.
In all our models, the magnetic field affects the equilibrium structure of the
torus mainly due to the magnetic pressure. In particular, an increasing
contribution of the magnetic field shifts the location of the maximum of the
rest-mass density towards inner regions of the disk. The total mass of the
system and the angular momentum are affected by the magnetic field in a complex
way, that depends on the black hole spin and the location of the inner radius
of the disk. The non-linear dynamical stability of the solutions presented in
this paper will be reported elsewhere.Comment: 17 pages, 5 figures, 1 tabl
Coherent resonant tunneling in ac fields
We have analyzed the tunneling transmission probability and electronic
current density through resonant heterostructures in the presence of an
external electromagnetic field. In this work, we compare two different models
for a double barrier : In the first case the effect of the external field is
taken into account by spatially dependent AC voltages and in the second one the
electromagnetic field is described in terms of a photon field that irradiates
homogeneously the whole sample. While in the first description the tunneling
takes place mainly through photo sidebands in the case of homogeneous
illumination the main effective tunneling channels correspond to the coupling
between different electronic states due to photon absorption and emission. The
difference of tunneling mechanisms between these configurations is strongly
reflected in the transmission and current density which present very different
features in both cases. In order to analyze these effects we have obtained,
within the Transfer Hamiltonian framework, a general expression for the
transition probability for coherent resonant tunneling in terms of the Green's
function of the system.Comment: 16 pages,Figures available upon request,to appear in Phys.Rev B (15
April 1996
Non-Native Non-\u3ci\u3eApis\u3c/i\u3e Bees Are More Abundant on Non-Native Versus Native Flowering Woody Landscape Plants
Urban ecosystems can support diverse communities of wild native bees. Because bloom times are conserved by geographic origin, incorporating some non-invasive non-native plants in urban landscapes can extend the flowering season and help support bees and other pollinators during periods when floral resources from native plants are limiting. A caveat, though, is the possibility that non-native plants might disproportionately host non-native, potentially invasive bee species. We tested that hypothesis by identifying all non-native bees among 11,275 total bees previously collected from 45 species of flowering woody landscape plants across 213 urban sites. Honey bees, Apis mellifera L., accounted for 22% of the total bees and 88.6% of the non-native bees in the collections. Six other non-native bee species, accounting for 2.86% of the total, were found on 16 non-native and 11 native woody plant species. Non-Apis non-native bees in total, and Osmia taurus Smith and Megachile sculpturalis (Smith), the two most abundant species, were significantly more abundant on non-native versus native plants. Planting of favored non-native hosts could potentially facilitate establishment and spread of non-Apis non-native bees in urban areas. Our host records may be useful for tracking those bees’ distribution in their introduced geographical ranges
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