11,856 research outputs found
Quantum Gauge Equivalence in QED
We discuss gauge transformations in QED coupled to a charged spinor field,
and examine whether we can gauge-transform the entire formulation of the theory
from one gauge to another, so that not only the gauge and spinor fields, but
also the forms of the operator-valued Hamiltonians are transformed. The
discussion includes the covariant gauge, in which the gauge condition and
Gauss's law are not primary constraints on operator-valued quantities; it also
includes the Coulomb gauge, and the spatial axial gauge, in which the
constraints are imposed on operator-valued fields by applying the
Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb and
spatial axial gauges to what we call
``common form,'' in which all particle excitation modes have identical
properties. We also show that, once that common form has been reached, QED in
different gauges has a common time-evolution operator that defines
time-translation for states that represent systems of electrons and photons.
By combining gauge transformations with changes of representation from
standard to common form, the entire apparatus of a gauge theory can be
transformed from one gauge to another.Comment: Contribution for a special issue of Foundations of Physics honoring
Fritz Rohrlich; edited by Larry P. Horwitz, Tel-Aviv University, and Alwyn
van der Merwe, University of Denver (Plenum Publishing, New York); 40 pages,
REVTEX, Preprint UCONN-93-3, 1 figure available upon request from author
Topology of the gauge-invariant gauge field in two-color QCD
We investigate solutions to a nonlinear integral equation which has a central
role in implementing the non-Abelian Gauss's Law and in constructing
gauge-invariant quark and gluon fields. Here we concern ourselves with
solutions to this same equation that are not operator-valued, but are functions
of spatial variables and carry spatial and SU(2) indices. We obtain an
expression for the gauge-invariant gauge field in two-color QCD, define an
index that we will refer to as the ``winding number'' that characterizes it,
and show that this winding number is invariant to a small gauge transformation
of the gauge field on which our construction of the gauge-invariant gauge field
is based. We discuss the role of this gauge field in determining the winding
number of the gauge-invariant gauge field. We also show that when the winding
number of the gauge field is an integer , the gauge-invariant
gauge field manifests winding numbers that are not integers, and are
half-integers only when .Comment: 26 pages including 6 encapsulated postscript figures. Numerical
errors have been correcte
Walls Inhibit Chaotic Mixing
We report on experiments of chaotic mixing in a closed vessel, in which a
highly viscous fluid is stirred by a moving rod. We analyze quantitatively how
the concentration field of a low-diffusivity dye relaxes towards homogeneity,
and we observe a slow algebraic decay of the inhomogeneity, at odds with the
exponential decay predicted by most previous studies. Visual observations
reveal the dominant role of the vessel wall, which strongly influences the
concentration field in the entire domain and causes the anomalous scaling. A
simplified 1D model supports our experimental results. Quantitative analysis of
the concentration pattern leads to scalings for the distributions and the
variance of the concentration field consistent with experimental and numerical
results.Comment: 4 pages, 3 figure
Slow decay of concentration variance due to no-slip walls in chaotic mixing
Chaotic mixing in a closed vessel is studied experimentally and numerically
in different 2-D flow configurations. For a purely hyperbolic phase space, it
is well-known that concentration fluctuations converge to an eigenmode of the
advection-diffusion operator and decay exponentially with time. We illustrate
how the unstable manifold of hyperbolic periodic points dominates the resulting
persistent pattern. We show for different physical viscous flows that, in the
case of a fully chaotic Poincare section, parabolic periodic points at the
walls lead to slower (algebraic) decay. A persistent pattern, the backbone of
which is the unstable manifold of parabolic points, can be observed. However,
slow stretching at the wall forbids the rapid propagation of stretched
filaments throughout the whole domain, and hence delays the formation of an
eigenmode until it is no longer experimentally observable. Inspired by the
baker's map, we introduce a 1-D model with a parabolic point that gives a good
account of the slow decay observed in experiments. We derive a universal decay
law for such systems parametrized by the rate at which a particle approaches
the no-slip wall.Comment: 17 pages, 12 figure
Nonholonomic systems with symmetry allowing a conformally symplectic reduction
Non-holonomic mechanical systems can be described by a degenerate
almost-Poisson structure (dropping the Jacobi identity) in the constrained
space. If enough symmetries transversal to the constraints are present, the
system reduces to a nondegenerate almost-Poisson structure on a ``compressed''
space. Here we show, in the simplest non-holonomic systems, that in favorable
circumnstances the compressed system is conformally symplectic, although the
``non-compressed'' constrained system never admits a Jacobi structure (in the
sense of Marle et al.).Comment: 8 pages. A slight edition of the version to appear in Proceedings of
HAMSYS 200
Effect of Native Defects on Optical Properties of InxGa1-xN Alloys
The energy position of the optical absorption edge and the free carrier
populations in InxGa1-xN ternary alloys can be controlled using high energy
4He+ irradiation. The blue shift of the absorption edge after irradiation in
In-rich material (x > 0.34) is attributed to the band-filling effect
(Burstein-Moss shift) due to the native donors introduced by the irradiation.
In Ga-rich material, optical absorption measurements show that the
irradiation-introduced native defects are inside the bandgap, where they are
incorporated as acceptors. The observed irradiation-produced changes in the
optical absorption edge and the carrier populations in InxGa1-xN are in
excellent agreement with the predictions of the amphoteric defect model
Disorder Potentials near Lithographically Fabricated Atom Chips
We show that previously observed large disorder potentials in magnetic
microtraps for neutral atoms are reduced by about two orders of magnitude when
using atom chips with lithographically fabricated high quality gold layers.
Using one dimensional Bose-Einstein condensates, we probe the remaining
magnetic field variations at surface distances down to a few microns.
Measurements on a 100 um wide wire imply that residual variations of the
current flow result from local properties of the wire.Comment: submitted on September 24th, 200
- …