489 research outputs found
Modified differentials and basic cohomology for Riemannian foliations
We define a new version of the exterior derivative on the basic forms of a
Riemannian foliation to obtain a new form of basic cohomology that satisfies
Poincar\'e duality in the transversally orientable case. We use this twisted
basic cohomology to show relationships between curvature, tautness, and
vanishing of the basic Euler characteristic and basic signature.Comment: 20 pages, references added, minor corrections mad
New Magnetic Excitations in the Spin-Density-Wave of Chromium
Low-energy magnetic excitations of chromium have been reinvestigated with a
single-Q crystal using neutron scattering technique. In the transverse
spin-density-wave phase a new type of well-defined magnetic excitation is found
around (0,0,1) with a weak dispersion perpendicular to the wavevector of the
incommensurate structure. The magnetic excitation has an energy gap of E ~ 4
meV and at (0,0,1) exactly corresponds to the Fincher mode previously studied
only along the incommensurate wavevector.Comment: 4 pages, 4 figure
QCD Corrections to QED Vacuum Polarization
We compute QCD corrections to QED calculations for vacuum polarization in
background magnetic fields. Formally, the diagram for virtual loops
is identical to the one for virtual loops. However due to
confinement, or to the growth of as decreases, a direct
calculation of the diagram is not allowed. At large we consider the
virtual diagram, in the intermediate region we discuss the role of
the contribution of quark condensates \left and at the
low-energy limit we consider the , as well as charged pion
loops. Although these effects seem to be out of the measurement accuracy of
photon-photon laboratory experiments they may be relevant for -ray
burst propagation. In particular, for emissions from the center of the galaxy
(8.5 kpc), we show that the mixing between the neutral pseudo-scalar pion
and photons renders a deviation from the power-law spectrum in the
range. As for scalar quark condensates \left and
virtual loops are relevant only for very high radiation density
and very strong magnetic fields of order .Comment: 15 pages, 4 figures; Final versio
Avoiding degenerate coframes in an affine gauge approach to quantum gravity
In quantum models of gravity, it is surmized that configurations with
degenerate coframes could occur during topology change of the underlying
spacetime structure. However, the coframe is not the true Yang--Mills type
gauge field of the translations, since it lacks the inhomogeneous gradient term
in the gauge transformations. By explicitly restoring this ``hidden" piece
within the framework of the affine gauge approach to gravity, one can avoid the
metric or coframe degeneracy which would otherwise interfere with the
integrations within the path integral. This is an important advantage for
quantization.Comment: 14 pages, Preprint Cologne-thp-1993-H
Running coupling in electroweak interactions of leptons from f(R)-gravity with torsion
The f(R)-gravitational theory with torsion is considered for one family of
leptons; it is found that the torsion tensor gives rise to interactions having
the structure of the weak forces while the intrinsic non-linearity of the f(R)
function provides an energy-dependent coupling: in this way, torsional f(R)
gravity naturally generates both structure and strength of the electroweak
interactions among leptons. This implies that the weak interactions among the
lepton fields could be addressed as a geometric effect due to the interactions
among spinors induced by the presence of torsion in the most general f(R)
gravity. Phenomenological considerations are addressed.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1012.5529 by other
author
Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions
We study the influence of short-range electron-electron interactions on
scaling behavior near the integer quantum Hall plateau transitions. Short-range
interactions are known to be irrelevant at the renormalization group fixed
point which represents the transition in the non-interacting system. We find,
nevertheless, that transport properties change discontinuously when
interactions are introduced. Most importantly, in the thermodynamic limit the
conductivity at finite temperature is zero without interactions, but non-zero
in the presence of arbitrarily weak interactions. In addition, scaling as a
function of frequency, , and temperature, , is determined by the
scaling variable (where is the exponent for the temperature
dependence of the inelastic scattering rate) and not by , as it would
be at a conventional quantum phase transition described by an interacting fixed
point. We express the inelastic exponent, , and the thermal exponent, ,
in terms of the scaling dimension, , of the interaction strength
and the dynamical exponent (which has the value ), obtaining
and .Comment: 9 pages, 4 figures, submitted to Physical Review
Hodge Theory on Metric Spaces
Hodge theory is a beautiful synthesis of geometry, topology, and analysis,
which has been developed in the setting of Riemannian manifolds. On the other
hand, spaces of images, which are important in the mathematical foundations of
vision and pattern recognition, do not fit this framework. This motivates us to
develop a version of Hodge theory on metric spaces with a probability measure.
We believe that this constitutes a step towards understanding the geometry of
vision.
The appendix by Anthony Baker provides a separable, compact metric space with
infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version,
to appear in Foundations of Computational Mathematics. Minor changes and
addition
Anomalous Hopping Exponents of Ultrathin Films of Metals
The temperature dependence of the resistance R(T) of ultrathin
quench-condensed films of Ag, Bi, Pb and Pd has been investigated. In the most
resistive films, R(T)=Roexp(To/T)^x, where x=0.75. Surprisingly, the exponent x
was found to be constant for a wide range of Ro and To in all four materials,
possibly implying a consistent underlying conduction mechanism. The results are
discussed in terms of several different models of hopping conduction.Comment: 6 pages, 5 figure
Particle Acceleration in Cosmic Sites - Astrophysics Issues in our Understanding of Cosmic Rays
Laboratory experiments to explore plasma conditions and stimulated particle
acceleration can illuminate aspects of the cosmic particle acceleration
process. Here we discuss the cosmic-ray candidate source object variety, and
what has been learned about their particle-acceleration characteristics. We
identify open issues as discussed among astrophysicists. -- The cosmic ray
differential intensity spectrum is a rather smooth power-law spectrum, with two
kinks at the "knee" (~10^15 eV) and at the "ankle" (~3 10^18 eV). It is unclear
if these kinks are related to boundaries between different dominating sources,
or rather related to characteristics of cosmic-ray propagation. We believe that
Galactic sources dominate up to 10^17 eV or even above, and the extragalactic
origin of cosmic rays at highest energies merges rather smoothly with Galactic
contributions throughout the 10^15--10^18 eV range. Pulsars and supernova
remnants are among the prime candidates for Galactic cosmic-ray production,
while nuclei of active galaxies are considered best candidates to produce
ultrahigh-energy cosmic rays of extragalactic origin. Acceleration processes
are related to shocks from violent ejections of matter from energetic sources
such as supernova explosions or matter accretion onto black holes. Details of
such acceleration are difficult, as relativistic particles modify the structure
of the shock, and simple approximations or perturbation calculations are
unsatisfactory. This is where laboratory plasma experiments are expected to
contribute, to enlighten the non-linear processes which occur under such
conditions.Comment: accepted for publication in EPJD, topical issue on Fundamental
physics and ultra-high laser fields. From review talk at "Extreme Light
Infrastructure" workshop, Sep 2008. Version-2 May 2009: adjust some wordings
and references at EPJD proofs stag
Onset of Superfluidity in 4He Films Adsorbed on Disordered Substrates
We have studied 4He films adsorbed in two porous glasses, aerogel and Vycor,
using high precision torsional oscillator and DC calorimetry techniques. Our
investigation focused on the onset of superfluidity at low temperatures as the
4He coverage is increased. Torsional oscillator measurements of the 4He-aerogel
system were used to determine the superfluid density of films with transition
temperatures as low as 20 mK. Heat capacity measurements of the 4He-Vycor
system probed the excitation spectrum of both non-superfluid and superfluid
films for temperatures down to 10 mK. Both sets of measurements suggest that
the critical coverage for the onset of superfluidity corresponds to a mobility
edge in the chemical potential, so that the onset transition is the bosonic
analog of a superconductor-insulator transition. The superfluid density
measurements, however, are not in agreement with the scaling theory of an onset
transition from a gapless, Bose glass phase to a superfluid. The heat capacity
measurements show that the non-superfluid phase is better characterized as an
insulator with a gap.Comment: 15 pages (RevTex), 21 figures (postscript
- âŠ